Problem 45
Question
Solve each equation using both the addition and multiplication properties of equality. Check proposed solutions. $$-5 x=-2 x-12$$
Step-by-Step Solution
Verified Answer
The solution to the equation \(-5x = -2x - 12\) is \(x = 4\)
1Step 1: Isolate x terms on one side of the equation
First, add \(2x\) to both sides of the equation to get rid of the \(x\) on the right hand side. This gives us \(-5x + 2x = -12\), which simplifies to \(-3x = -12\).
2Step 2: Solve for x
Next, we divide every term by \(-3\) to solve for \(x\). This gives \(x = 4\).
3Step 3: Check the solution
We substitute 4 into the original equation \(-5x = -2x - 12\). This gives \(-5(4) = -2(4) - 12\) which simplifies to \(-20 = -8 - 12\), and further simplifies to \(-20 = -20\). Since both sides are equal, our solution is correct.
Other exercises in this chapter
Problem 45
Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. $$3 x \geq-21$$
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Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions. $$6 y+3-5 y=14$$
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Solve equation and check your proposed solution. Begin your work by rewriting each equation without fractions. \(\frac{x-3}{5}-1=\frac{x-5}{4}\)
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