4.5(8 - x) + 36 = 102 - 2.5(3x + 24)
1 answer:
Answer:
x = -10
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS Equality Properties Step-by-step explanation:
<u>Step 1: Define equation</u>
4.5(8 - x) + 36 = 102 - 2.5(3x + 24)
<u>Step 2: Solve for </u><em><u>x</u></em>
Distribute: 36 - 4.5x + 36 = 102 - 7.5x - 60 Combine like terms: -4.5x + 72 = -7.5x + 42 Add 7.5x on both sides: 3x + 72 = 42 Subtract 72 on both sides: 3x = -30 Divide 3 on both sides: x = -10
<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>: 4.5(8 - -10) + 36 = 102 - 2.5(3(-10) + 24) Simplify: 4.5(8 + 10) + 36 = 102 - 2.5(3(-10) + 24) Multiply: 4.5(8 + 10) + 36 = 102 - 2.5(-30 + 24) Add: 4.5(18) + 36 = 102 - 2.5(-6) Multiply: 81 + 36 = 102 + 15 Add: 117 = 117 Here we see that 117 does indeed equal to 117.
∴ x = -10 is a solution of the equation.
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