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Solving Multi-Step Equations

Solving Multi-Step Equations 1.7 - Solution

arrow_back Return to Solving Multi-Step Equations
a
Start by multiplying 44 into the parentheses. We can then solve for xx using inverse operations.
4(x3)+2=104(x - 3) + 2 = 10
4x43+2=104 \cdot x - 4 \cdot 3 + 2 = 10
4x12+2=104x - 12 + 2 = 10
4x10=104x - 10 = 10
4x=204x = 20
x=5x = 5
b
First, multiply 33 to the terms inside parentheses. Then, gather all the variables on one side and the constants on the other.
2x+7=-4+3(8+5x)2x + 7 = \text{-} 4 + 3(8 + 5x)
2x+7=-4+38+35x2x + 7 = \text{-} 4 + 3 \cdot 8 + 3 \cdot 5x
2x+7=-4+24+15x2x + 7 = \text{-} 4 + 24 + 15x
2x+7=20+15x2x + 7 = 20 + 15x
7=20+13x7 = 20 + 13x
-13=13x\text{-} 13 = 13x
13x=-1313x=\text{-} 13
x=-1x = \text{-} 1
c
On the left-hand side we can start by distributing 2.2. Then we remove the parentheses on the left-hand side and change signs on the terms inside.
5+2(-7+x)=-6(-x+8)5 + 2(\text{-} 7 + x) = \text{-} 6 - (\text{-} x + 8)
5+2(-7)+2x=-6(-x+8)5 + 2(\text{-}7) + 2 \cdot x = \text{-} 6 - (\text{-} x + 8)
514+2x=-6(-x+8)5 -14 + 2x = \text{-} 6 - (\text{-} x + 8)
514+2x=-6+x85 -14 + 2x = \text{-} 6 +x - 8
-9+2x=x14\text{-} 9 + 2x = x - 14
2x=x52x = x - 5
x=-5x= \text{-} 5