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Chapter 4: Problem 59

$$\text { Solve: } 2(x+3)=24-2(x+4)$$

Short Answer

Expert verified
The solution to the equation is \(x = 2.5\).

Step by step solution

01

Distribute the 2

By employing the distributive property, multiply the 2 into each term in the parentheses on each side of the equation to obtain \(2x + 6 = 24 - 2x - 8\).
02

Simplify each side

Simplify each side of the equation in order to gather like terms. On the left, there are no simplifications to be done. On the right, 24-8 results into 16. This yields \(2x + 6 = 16 - 2x\).
03

Group all x terms on one side

To solve for x, all the terms containing x should be grouped on one side of the equation. To do so, add \(2x\) to both sides, resulting into \(4x + 6 = 16\).
04

Isolate x

In order to get x by itself, subtract 6 from both sides of the equation. The equation simplifies to \(4x = 10\).
05

Solve for x

Finally, to solve for x, divide both sides by 4 to isolate x. This gives \(x = 2.5\).

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Most popular questions from this chapter

Multiply both sides of \(x-5 y=3\) by \(-4\) and simplify.

Write the slope-intercept form of the equation of the Tine passing through \((-5,6)\) and \((3,-10)\)

In Exercises \(61-68,\) solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{aligned} 1.25 x-1.5 y &=2 \\ 3.5 x-1.75 y &=10.5 \end{aligned}\right.$$

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. When I use graphing to solve an inconsistent system, the lines should look parallel, and I can always use slope to confirm that they really are.

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}2 x-3 y=7 \\ 3 x+5 y=1\end{array}\right.$$
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