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AQA GCSE · Question 08 · Algebra
Solve 7x - 22 = 4x + 29
Solve 7x - 22 = 4x + 29
How to approach this question
The goal is to isolate the variable `x`.
1. Start by moving all the terms containing `x` to one side of the equation. You can do this by subtracting the smaller `x` term (4x) from both sides.
2. Next, move all the constant terms (the numbers) to the other side of the equation.
3. Finally, divide by the coefficient of `x` to find the value of `x`.
Full Answer
Step 1: Get all the x terms on one side. Subtract 4x from both sides.
7x - 4x - 22 = 4x - 4x + 29
3x - 22 = 29
Step 2: Get all the constant terms on the other side. Add 22 to both sides.
3x - 22 + 22 = 29 + 22
3x = 51
Step 3: Solve for x. Divide both sides by 3.
x = 51 / 3
x = 17
This is a linear equation with the variable `x` on both sides.
The equation is: 7x - 22 = 4x + 29
1. To group the `x` terms, we can subtract 4x from both sides:
(7x - 4x) - 22 = (4x - 4x) + 29
3x - 22 = 29
2. To group the constant terms, we can add 22 to both sides:
3x - 22 + 22 = 29 + 22
3x = 51
3. To solve for `x`, we divide both sides by 3:
x = 51 / 3
To calculate 51 ÷ 3, you can split 51 into 30 + 21. 30 ÷ 3 = 10 and 21 ÷ 3 = 7. So, 10 + 7 = 17.
x = 17
Common mistakes
✗ Making sign errors when moving terms across the equals sign. For example, subtracting 29 instead of adding 22.
✗ Incorrectly combining terms, e.g., 7x - 4x = 11x.
✗ Errors in the final division, e.g., 51/3.
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