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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Writing Linear Equations

Test your skills with clear equation practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art representing a trivia quiz about Equation Writing Lab for middle school math students.

Which equation correctly represents the statement 'A number increased by 5 equals 12'?
x + 5 = 12
5x = 12
12 + 5 = x
x - 5 = 12
The equation x + 5 = 12 accurately translates the phrase 'a number increased by 5 equals 12'. The other options incorrectly apply multiplication or subtraction, which does not match the intended operation.
Solve for x in the equation 3 + x = 10.
x = 7
x = 13
x = 3
x = 10
Subtracting 3 from 10 gives x = 7, which satisfies the equation. The other choices result from misapplying the basic arithmetic required.
Which equation represents the phrase 'Subtract 3 from a number to get 9'?
9 - x = 3
x - 3 = 9
x + 3 = 9
3 - x = 9
The equation x - 3 = 9 correctly reflects the operation of subtracting 3 from an unknown number. The other equations either reverse the subtraction or use addition.
Solve for x in the equation x - 4 = 6.
x = 10
x = 2
x = 4
x = 6
Adding 4 to both sides of the equation x - 4 = 6 results in x = 10, which is the correct balanced solution. The other answers stem from incorrect arithmetic operations.
Which is the correct equation for the statement 'Four is added to a number to give nine'?
x + 4 = 9
x - 4 = 9
9 + 4 = x
4x = 9
The equation x + 4 = 9 directly matches the statement by adding 4 to the unknown number to yield 9. The alternatives introduce errors such as subtraction or multiplication instead of addition.
Which equation represents the phrase 'The sum of twice a number and 3 is 11'?
2x + 3 = 11
2x - 3 = 11
2x + 11 = 3
x + 3 = 11
Twice a number is expressed as 2x, and adding 3 gives the equation 2x + 3 = 11, which correctly translates the phrase. The remaining options misapply the operations or the constants.
Translate 'Seven less than three times a number equals 11' into an equation.
3x + 7 = 11
3(x - 7) = 11
3x - 7 = 11
7 - 3x = 11
The correct translation is 3x - 7 = 11, where three times a number is 3x and 'seven less than' implies subtracting 7. The other options either add where subtraction is required or misplace the subtraction entirely.
Write the equation for 'A number doubled and then increased by 4 equals 16.'
2x + 4 = 16
2x - 4 = 16
x + 4 = 16
x - 4 = 16
Doubling a number gives 2x, and adding 4 leads directly to the equation 2x + 4 = 16, which is the proper translation. The other choices misrepresent either the multiplication or the addition step.
After distributing 2 in the equation 5 + 2(x - 1) = 3x, which simplified equation is correct?
2x + 3 = 3x
2x - 3 = 3x
2x + 5 = 3x
x + 3 = 3x
Distributing 2 into (x - 1) yields 2x - 2, and adding 5 gives 2x + 3, resulting in the equation 2x + 3 = 3x. The other options reflect errors in the distribution or consolidation process.
Which equation is equivalent to 4(x - 2) = 2x + 8 after simplifying?
4x - 8 = 2x + 8
4x + 8 = 2x - 8
4x - 8 = 2x - 8
4x + 8 = 2x + 8
Expanding 4(x - 2) gives 4x - 8, which when set equal to 2x + 8, forms the correct equation. The other alternatives misplace the signs and constants.
Solve for x in the equation 3(x + 2) = 2x + 9.
x = 3
x = 2
x = 9
x = -3
Expanding the left side gives 3x + 6, and setting it equal to 2x + 9 leads to x + 6 = 9 and thus x = 3. The other choices do not satisfy the steps of the solution.
What equation represents 'The difference between a number and 4 is equal to twice that number minus 10'?
x - 4 = 2x - 10
x + 4 = 2x - 10
x - 4 = 2x + 10
4 - x = 10 - 2x
The correct translation uses x - 4 for 'a number minus 4' and 2x - 10 for 'twice that number minus 10'. The other options incorrectly apply the operations or reverse the subtraction order.
Write the equation for 'Four times a number decreased by 2 equals three times the number increased by 4.'
4x - 2 = 3x + 4
4x + 2 = 3x + 4
4x - 2 = 3x - 4
4(x - 2) = 3(x + 4)
Translating the statement gives 4x - 2 for 'four times a number decreased by 2' and 3x + 4 for 'three times the number increased by 4'. The other choices either adjust the signs incorrectly or incorrectly apply distribution.
Solve the equation x/2 + 3 = 7.
x = 8
x = 10
x = 14
x = 4
Subtracting 3 from 7 gives x/2 = 4, and multiplying both sides by 2 results in x = 8. The alternative answers do not follow the correct inverse operations.
Translate 'A number decreased by 8 equals one-half of that number plus 2' into an equation.
x - 8 = (1/2)x + 2
x + 8 = (1/2)x + 2
x - 8 = 2x + 2
(1/2)(x - 8) = x + 2
The phrase directly converts to x - 8 on the left side and (1/2)x + 2 on the right side, forming the equation x - 8 = (1/2)x + 2. The other options misinterpret the order or grouping of operations.
From the statement 'Six more than twice a number is equal to three times the number decreased by 4', write the corresponding equation.
2x + 6 = 3x - 4
2x - 6 = 3x - 4
3x + 6 = 2x - 4
3x + 4 = 2x - 6
The correct translation involves taking twice a number (2x), adding 6, and setting it equal to three times the number minus 4, which gives 2x + 6 = 3x - 4. The other options either reverse the operations or misplace the constants.
Convert the phrase 'The sum of a number and its double is 27' into an equation and solve for x.
x = 9
x = 27
x = 3
x = 15
Translating the phrase gives x + 2x = 27, which simplifies to 3x = 27. Dividing both sides by 3 results in x = 9. The other options arise from miscalculations of the arithmetic.
A teacher states: 'Half of a number increased by 7 equals 15.' Which equation correctly represents this statement?
(x/2) + 7 = 15
x/2 = 7 + 15
(x + 7)/2 = 15
x + (7/2) = 15
The phrase 'half of a number' is represented by x/2, and when increased by 7, it forms the equation (x/2) + 7 = 15. The alternative options incorrectly alter the structure of the expression.
Derive the equation from: 'After subtracting 9 from three times a number, the result is twice the number plus 3.'
3x - 9 = 2x + 3
3x + 9 = 2x + 3
3x - 9 = 2x - 3
3x + 9 = 2x - 3
Subtracting 9 from three times the number yields 3x - 9, which is stated to equal twice the number plus 3 (2x + 3). The other options misapply the subtraction or use incorrect signs.
Determine the balanced equation for the scenario 'Five times a number minus 11 equals twice the number plus 4.'
5x - 11 = 2x + 4
5x + 11 = 2x + 4
5x - 11 = 2x - 4
5x + 11 = 2x - 4
The correct equation directly translates 'five times a number' as 5x, subtracting 11 gives 5x - 11, and setting that equal to 'twice the number plus 4' results in 2x + 4. The other alternatives have misapplied the addition or subtraction of constants.
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Study Outcomes

  1. Construct balanced linear equations from given scenarios.
  2. Analyze equation components to identify and correct imbalances.
  3. Apply algebraic strategies to transform unbalanced equations into balanced ones.
  4. Evaluate the accuracy of constructed equations through self-assessment.
  5. Demonstrate improved proficiency in solving linear equations for test readiness.

Practice: Writing Linear Equations Cheat Sheet

  1. Master the slope-intercept form - Dive into y = mx + b, where m is the slope and b is the y‑intercept. This friendly formula makes graphing linear relationships a breeze and helps you predict outputs in style. Slope-Intercept Form
  2. Calculate slope like a pro - Use two points (x₝, y₝) and (x₂, y₂) with m = (y₂ - y₝)/(x₂ - x₝) to find how steep your line is. Once you crack this, every hill and valley in your graphs becomes crystal clear. How to Write Linear Equations?
  3. Conquer point-slope form - Employ y - y₝ = m(x - x₝) when you know a point on the line and its slope. It's like having a treasure map: one landmark and a direction guide you right to your equation. Point-Slope Form
  4. Switch seamlessly between forms - Convert from point-slope to slope-intercept (and back!) in just a few steps. This flexibility means you can tackle any algebra problem thrown your way without breaking a sweat. Converting Among Forms
  5. Translate real-world scenarios - Identify the slope and y‑intercept from word problems to build equations that model everyday situations, from pizza sales to temperature changes. Math suddenly feels like solving a detective mystery! Writing Linear Equations From Situations and Graphs
  6. Solve equations with confidence - Isolate the variable using inverse operations, keep everything balanced, and verify by plugging your solution back in. It's like checking your work on a treasure hunt - no detail goes unnoticed! Solve Linear Equations Practice
  7. Write parallel and perpendicular lines - Remember that parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals. With this trick, you can craft any lineup of perfect angles. Writing Linear Equations
  8. Tackle word problems fearlessly - Practice translating real-life stories into linear equations. As you decode age puzzles or speed-distance dilemmas, you'll sharpen your modeling skills and become a math superhero. Linear Equations Word Problems
  9. Reinforce with online drills - Jump into interactive exercises to solidify your grasp on writing and solving linear equations. Regular practice boosts both accuracy and speed, turning you into a classroom rockstar. Linear Equations Practice Problems
  10. Always double‑check your answers - Plug solutions back into the original equation to confirm they work every time. This final sweep catches sneaky mistakes and builds your confidence for test day. Algebra - Linear Equations (Practice Problems)
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