Solving Equations with Variables on Both Sides
This worksheet focuses on solving linear equations where variables appear on both sides of the equation, including those with distributive property and fractions.
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Solving Equations with Variables on Both Sides
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Solve each equation for the given variable. Show all your work. Simplify your answers.
1. Solve for x: 5x + 3 = 2x + 15
2. Solve for y: 7y - 10 = 3y + 6
3. Fill in the blank to complete the solution steps for the equation: 3(x + 4) = 5x - 2
3x + 12 = 5x - 2
12 = 2x - 2
= 2x
x =
4. Solve for m: 2(m - 3) + 4 = 5m - 8
5. Which of the following is the correct solution for the equation 6 - 2(w + 1) = 4w - 8?
w = 1
w = 2
w = 3
w = 4
6. Solve for p: (1/2)p + 5 = (3/4)p - 1
7. Solve for z: (2/3)(z - 4) = (1/6)z + 2
8. The equation 3x + 7 = 3x - 5 has no solution.
True
False
9. The equation 4(x + 1) = 4x + 4 has infinitely many solutions.
True
False
10. Consider the following equation: 2x + 1 = x + 3. Imagine a balance scale where each 'x' represents an unknown weight and '1' represents a unit weight. Draw an illustration of this equation using the balance scale concept.
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