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Chapter 2: Problem 37

Solve each equation. $$8(u+1.5)-7 u=4.9$$

Short Answer

Expert verified
u = -7.1

Step by step solution

01

Distribute 8

Distribute the 8 through the parentheses: \[ 8(u + 1.5) = 8u + 12 \ 8u + 12 - 7u = 4.9 \]
02

Combine like terms

Combine the terms involving \(u\): \[ 8u - 7u + 12 = 4.9 \ u + 12 = 4.9 \]
03

Isolate u

Subtract 12 from both sides to solve for \(u\): \[ u + 12 - 12 = 4.9 - 12 \ u = -7.1 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
When solving linear equations, one of the first steps is often to use the distributive property. This property allows us to simplify expressions by distributing a multiplication over addition or subtraction within parentheses. In the given problem, we have the expression \( 8(u + 1.5) \). To simplify this, we multiply both \(u\) and \(1.5\) by 8:

  • \(8 \times u = 8u\)

  • \(8 \times 1.5 = 12\)

So, \(8(u + 1.5)\) becomes \(8u + 12\). Now our equation looks like this: \[ 8u + 12 - 7u = 4.9 \]. By distributing, we've removed the parentheses and simplified the equation.

Combining Like Terms
The next step in solving the equation is to combine like terms. Like terms are terms that contain the same variable raised to the same power. In our equation, \(8u\) and \(-7u\) are like terms because they both involve the variable \(u\). To combine these terms, we simply add or subtract their coefficients:

  • \(8u - 7u = u\)

After combining these like terms, the equation simplifies to \(u + 12 = 4.9\). This step makes the equation easier to solve by reducing the number of terms.

Isolating the Variable
Finally, we need to isolate the variable to solve for it. In this case, we need to solve for \(u\). Our simplified equation is \(u + 12 = 4.9\). To isolate \(u\), we need to get it by itself on one side of the equation. We can do this by subtracting 12 from both sides:

  • \(u + 12 - 12 = 4.9 - 12\)

  • \(u = -7.1\)

So, \(u\) is equal to \(-7.1\). By carefully isolating the variable, we've successfully solved the equation.

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Most popular questions from this chapter

Graph each inequality on the number line and write in interval notation. (a) \(x<-2\) (b) \(\quad x \geq-3.5\) (c) \(x \leq \frac{2}{3}\)

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Translate and solve. Then write the solution in interval notation and graph on the number line. Fifteen less than \(a\) is at least \(-7 .\)

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