Math  /  Algebra

QuestionSolve the following and graph the solutions: 3x+7>1 or 3x+7<1x<83 or x>2\begin{array}{c} -3 x+7>-1 \text { or }-3 x+7<1 \\ x<\frac{8}{3} \text { or } x>2 \end{array}
x<83 or x>2x<\frac{8}{3} \text { or } x>2 x<83 or x>2x<\frac{8}{3} \text { or } x>2
x<83 or x>2x<\frac{8}{3} \text { or } x>2
undefined24<83 or x>2\xrightarrow[2]{4<\frac{8}{3} \text { or } x>2}

Studdy Solution

STEP 1

1. The problem involves solving a compound inequality.
2. The compound inequality is composed of two separate inequalities connected by the logical operator "or".
3. The solution set needs to be graphed on a number line.

STEP 2

1. Solve each inequality separately.
2. Combine the solutions using the "or" operator.
3. Graph the solution set on a number line.

STEP 3

Solve the first inequality: 3x+7>1 -3x + 7 > -1 .
Subtract 7 from both sides:
3x>17 -3x > -1 - 7
Simplify:
3x>8 -3x > -8
Divide both sides by 3-3 and reverse the inequality sign:
x<83 x < \frac{8}{3}

STEP 4

Solve the second inequality: 3x+7<1 -3x + 7 < 1 .
Subtract 7 from both sides:
3x<17 -3x < 1 - 7
Simplify:
3x<6 -3x < -6
Divide both sides by 3-3 and reverse the inequality sign:
x>2 x > 2

STEP 5

Combine the solutions from the two inequalities using the "or" operator:
The solution is x<83 x < \frac{8}{3} or x>2 x > 2 .

STEP 6

Graph the solution set on a number line:
1. Draw a number line.
2. Mark the points 83 \frac{8}{3} and 2 2 .
3. Use an open circle at 83 \frac{8}{3} and shade to the left to represent x<83 x < \frac{8}{3} .
4. Use an open circle at 2 2 and shade to the right to represent x>2 x > 2 .

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