Isolating Variables in Algebraic Equations

Grade 10 math worksheet focusing on isolating variables in linear, quadratic, and literal equations, including word problems.

Grade 10 Math AlgebraIsolating Variables

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3 Short AnswerFill in the BlanksMatchingMultiple Choice

Standards

CCSS.MATH.CONTENT.HSA.CED.A.1CCSS.MATH.CONTENT.HSA.REI.B.3CCSS.MATH.CONTENT.HSA.REI.B.4.A

Topics

AlgebraIsolating VariablesEquationsGrade 10Math

8 sections · Free to use · Printable

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Isolating Variables in Algebraic Equations

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Read each question carefully and follow the instructions to isolate the specified variable. Show all your work.

1. Isolate 'x' in the equation: 5x + 12 = 3x - 4

2. Solve for 'y' in the equation: 7(y - 3) = 2y + 9

3. To solve the formula for the area of a rectangle, A = lw, for 'l', you would both sides by 'w'.

4. If you want to isolate 'h' in the formula for the volume of a cylinder, V = πr²h, the first step is to both sides by πr².

Match each formula with the correct isolated variable.

5. P = 2l + 2w (for l)

a. t = I / (Pr)

6. I = Prt (for t)

b. F = (9/5)C + 32

7. C = (5/9)(F - 32) (for F)

c. l = (P - 2w) / 2

8. Isolate 'x' in the equation: x² - 9 = 0

9. Solve for 'x' in the equation: 2x² = 50

10. The perimeter of a square is given by the formula P = 4s, where 's' is the side length. If the perimeter of a square is 36 cm, what is the side length?

4 cm

6 cm

9 cm

12 cm

11. Isolate 'y' in the equation: ax + by = c

12. Solve for 'r' in the equation: A = P(1 + rt)