Type the correct answer in the box. Use numerals instead of words. What value of [tex]$x$[/tex] makes this equation true? [tex]$-2 x+3=-15$[/tex] [tex]$x=$[/tex]
Answer (2)
Subtract 3 from both sides: − 2 x = − 18 .
Divide both sides by -2: x = − 2 − 18 .
Simplify the fraction.
The solution is: 9
Explanation
Understanding the Problem We are given the equation − 2 x + 3 = − 15 , and our goal is to find the value of x that makes this equation true. We will isolate x by performing algebraic operations on both sides of the equation.
Isolating the x term First, we subtract 3 from both sides of the equation to isolate the term with x :
− 2 x + 3 − 3 = − 15 − 3 − 2 x = − 18
Solving for x Next, we divide both sides of the equation by -2 to solve for x :
− 2 − 2 x = − 2 − 18 x = 9
Final Answer Therefore, the value of x that makes the equation true is 9.
Examples
Imagine you are trying to determine how many hours you need to work this week to earn a specific amount of money. If you earn $15 per hour and already have $3, you can use the equation -2x + 3 = -15 to determine how many additional hours you need to work if you need to pay off a $18 debt. This algebraic approach helps in managing finances and planning work schedules effectively.
The value of x that makes the equation − 2 x + 3 = − 15 true is 9 . We reached this conclusion by isolating x using algebraic operations. First, we subtracted 3 from both sides and then divided by -2.
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