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Chapter 6: Problem 100

Solve each equation. \(2(5 x+58)=10 x+4(21 \div 3.5-11)\)

Short Answer

Expert verified
The equation has no solution.

Step by step solution

01

Distribute on the left side

The first step is to distribute the multiplication by 2 on the left side of the equation. \(2 \times 5x = 10x\) and \(2 \times 58 = 116\). So the left side of the equation becomes \(10x + 116\).
02

Simplify the right side

On the right side of the equation, first do the division inside the parentheses \((21 \div 3.5 = 6)\) and then subtract 11 from the result \((6 - 11 = -5)\). After that, multiply this result by 4 \(4 \times -5 = -20\). So, the right side of the equation becomes \(10x - 20\).
03

Equate both sides

Now, the equation simplifies to \(10x + 116 = 10x - 20\)
04

Solve for x

Subtract \(10x\) from both sides of the equation. This will leave us with \(116 = -20\). However, this is not a valid solution, meaning the equation has no solution.

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