Problem

Solve each equation and inequality. Write the sol…

03:54

Problem 99 Hard Difficulty

Solve each equation and inequality. Write the solution set of each inequality in interval notation and graph it.
a. $\frac{3}{8}+\frac{b}{3}>\frac{5}{12}$
b. $\frac{3}{8}+\frac{b}{3}=\frac{5}{12}$

Answer

$$\text { a. }\left(\frac{1}{8}, \infty\right)$$
b. $\frac{1}{8}$

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Precalculus

Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 7

Solving Inequalities

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Video Transcript

there are two parts to this next problem. Part A. We will use properties of inequality to solve inequality. But for Part B, we're going to use properties of equality to solve the equation. Let's begin with part A 3/8 plus be divided by three is greater than 5 12 First, let's eliminate the fractions by multiplying both sides of the inequality by the least common denominator of three. Eighth be divided by three and 5 12 At least common denominator is going to be 24. Multiply both sides of the inequality by 24 and we will have on the left 24 times. 3/8 is nine plus 24 times beat about it by three is eight b is greater than on the right. 5 12 times 24 is 10 From here. We want to isolate eight b, so we're going to undo the addition of nine by subtracting nine from both sides of the inequality. Eight. B is greater than one. Finally undo the product of eight and be using the inverse operation and divide both sides of the inequality by eight. This leaves us with the inequality of B is greater than 18 an interval notation. We're going to open the interval at 1/8 with a parentheses. E. We're going to close the interval at positive Infinity, also with the parentheses. E Remember, the parentheses indicates that 1/8 is not part of the solution set on our number line. Start with an open circle at 1/8 and shade all values on the number line that are greater than 1/8. So that's all values to the right of 1/8. No, let's move on to Part B, where we're going to use similar inverse operations. But properties of equality to solve the equation 3/8 plus be divided by three is equal to 5 12 We're going to start the same way and eliminate the fractions by multiplying both sides of the equation by the least common denominator. 24. Okay, on the left, we have 24 times 3/8 which is nine plus 24 times be divided by three. Eight B. This is equal to 5 12 times 24 which is 10 next under the addition of nine and subtract nine from both sides of the Equation eight b equals 10 minus nine, which is one and finally undo the product of eight and be using the inverse operation and divide both sides of the equation by eight. B is equal to 1/8.

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