What is x if 5(2x - 3) - 4(3x - 2) = 18?

Question:

What is x if 5(2x - 3) - 4(3x - 2) = 18?

Parentheses in an Equation:

When a number is written next to terms in parentheses, we must obey the distribution principle as a necessary first step. This means that we multiply the number next to the parentheses by each of the terms in the parentheses. For example, 3(x + y) = 3x + 3y.

Answer and Explanation: 1

If {eq}5(2x - 3) - 4(3x - 2) = 18 {/eq}, then x equals -12.5.

The first step to finding our answer is to use the distributive property to address the multiplication with our terms in parentheses. This means we have to multiply the number outside the parentheses by each of the terms inside the parentheses.

  • {eq}5(2x - 3) - 4(3x - 2) = 18 {/eq}
  • {eq}5(2x) - 5(3) - 4(3x) - 4(-2) = 18 {/eq}
  • {eq}10x - 15 - 12x - (-8) = 18 ? {/eq}

However, when we subtract a negative, it is the same as adding a positive. This gives us the following equation.

  • {eq}10x - 15 - 12x + 8 = 18 {/eq}

Next, we group the like terms and perform the math using them.

  • {eq}(10x - 12x) + (8 - 15) = 18 {/eq}
  • {eq}-2x + (-7) = 18 {/eq}

Adding a negative is the same as subtracting a positive, changing our equation to the following.

  • {eq}-2x - 7 = 18 {/eq}

Now, we can isolate the term with the variable by adding 7 to both sides of the equation.

  • {eq}-2x - 7 + (7) = 18 + 7 {/eq}
  • {eq}-2x = 25 {/eq}

Finally, we divide both sides of the equation by -2 to get our answer.

  • {eq}-2x \div -2 = 25 \div -2 ? {/eq}
  • {eq}x = -12.5 {/eq}

Learn more about this topic:

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What is PEMDAS? - Definition, Rule & Examples

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Chapter 26 / Lesson 14
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This lesson will discuss an important acronym for the order of operations in mathematics. Without these guidelines given in PEMDAS, the accurate and objective nature of mathematical calculation could not exist.


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