Answer:
x = 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
5 - 7(2 - x) = 31 - 4(2x - 5)
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute: 5 - 14 + 7x = 31 - 8x + 20
- Subtract/Add: -9 + 7x = -8x + 51
- Add 8x on both sides: -9 + 15x = 51
- Add 9 to both sides: 15x = 60
- Divide 15 on both sides: x = 4
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 5 - 7(2 - 4) = 31 - 4(2(4) - 5)
- (Parenthesis) Multiply: 5 - 7(2 - 4) = 31 - 4(8 - 5)
- (Parenthesis) Subtract: 5 - 7(-2) = 31 - 4(3)
- Multiply: 5 + 14 = 31 - 12
- Add/Subtract: 19 = 19
Here we see that 19 does indeed equal 19.
∴ x = 4 is the solution to the equation.