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Match each inequality to its solution.

a. [tex]\( -3x \ \textgreater \ -36 \)[/tex]

b. [tex]\( b + 5 \ \textgreater \ 23 \)[/tex]

c. [tex]\( 1 + 7n \geq -90 \)[/tex]

d. [tex]\( \frac{x}{2} - 2 \ \textgreater \ 1 \)[/tex]

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Quiz 4.2.1 - One and Two-Step Inequalities
Week 4 - Assignment 3 of 4


Sagot :

Let's solve each of the given inequalities step-by-step and match them to their solutions.

### Inequality 1: [tex]\(-3x > -36\)[/tex]

1. Step 1: Isolate [tex]\(x\)[/tex] by dividing both sides by [tex]\(-3\)[/tex]. Remember that dividing by a negative number reverses the inequality sign.
[tex]\[ x < 12 \][/tex]

### Inequality 2: [tex]\(b + 5 > 23\)[/tex]

1. Step 1: Isolate [tex]\(b\)[/tex] by subtracting 5 from both sides.
[tex]\[ b > 18 \][/tex]

### Inequality 3: [tex]\(1 + 7n \geq -90\)[/tex]

1. Step 1: Subtract 1 from both sides to isolate the term with [tex]\(n\)[/tex].
[tex]\[ 7n \geq -91 \][/tex]

2. Step 2: Divide both sides by 7.
[tex]\[ n \geq -13 \][/tex]

### Inequality 4: [tex]\(\frac{x}{2} - 2 > 1\)[/tex]

1. Step 1: Add 2 to both sides to isolate the term with [tex]\(x\)[/tex].
[tex]\[ \frac{x}{2} > 3 \][/tex]

2. Step 2: Multiply both sides by 2.
[tex]\[ x > 6 \][/tex]

### Matching the Solutions:

- 1. [tex]\(-3x > -36\)[/tex] corresponds to [tex]\(\boxed{x < 12}\)[/tex].
- 2. [tex]\(b + 5 > 23\)[/tex] corresponds to [tex]\(\boxed{b > 18}\)[/tex].
- 3. [tex]\(1 + 7n \geq -90\)[/tex] corresponds to [tex]\(\boxed{n \geq -13}\)[/tex].
- 4. [tex]\(\frac{x}{2} - 2 > 1\)[/tex] corresponds to [tex]\(\boxed{x > 6}\)[/tex].

So, the matched inequalities and their solutions are:

a. [tex]\(x < 12\)[/tex] [tex]\(\rightarrow\)[/tex] 1. [tex]\(-3x > -36\)[/tex]

b. [tex]\(b > 18\)[/tex] [tex]\(\rightarrow\)[/tex] 2. [tex]\(b + 5 > 23\)[/tex]

c. [tex]\(n \geq -13\)[/tex] [tex]\(\rightarrow\)[/tex] 3. [tex]\(1 + 7n \geq -90\)[/tex]

d. [tex]\(x > 6\)[/tex] [tex]\(\rightarrow\)[/tex] 4. [tex]\(\frac{x}{2} - 2 > 1\)[/tex]

I hope this helps you understand how to solve and match these inequalities with their respective solutions!