Question

Solve this inequality. Show or explain all steps for full credit. Then draw

graph.
4(7x - 26) < 64 and 5(19+ 2x) >-65

Answer 1

The inequalities 4(7x - 26) < 64 and 5(19+ 2x) >-65 are solved by distributing, combining like terms, and dividing, resulting in the solution -16 < x < 6. The graph of these inequalities is a number line with open circles at x = -16 and x = 6 and the region between them shaded.

Step-by-step explanation:

To solve the inequality 4(7x - 26) < 64, follow these steps:

1. Distribute the 4 into the parentheses: 28x - 104 < 64.
2. Add 104 to both sides: 28x < 168.
3. Divide both sides by 28: x < 6.

For the second inequality 5(19+ 2x) > -65, the steps are:

1. Distribute the 5 into the parentheses: 95 + 10x > -65.
2. Subtract 95 from both sides: 10x > -160.
3. Divide both sides by 10: x > -16.

Combine the two solutions to find the values of x that satisfy both inequalities: -16 < x < 6.

To graph these inequalities, draw a number line, plot the points x = -16 (with an open circle because it is a strict inequality) and x = 6 (also with an open circle), and shade the region between these two points to represent all the x values that satisfy the inequalities.