Question

solve the inequality and graph the solution.
7(d + 1) - 4 ≤ 10
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 7\), \(b=d\), \(c = 1\).
\(7(d + 1)-4=7d+7 - 4=7d + 3\). So the inequality becomes \(7d+3\leq10\).

Step2: Isolate the term with \(d\)

Subtract 3 from both sides of the inequality.
\(7d+3-3\leq10 - 3\), which simplifies to \(7d\leq7\).

Step3: Solve for \(d\)

Divide both sides of the inequality by 7. Since \(7>0\), the direction of the inequality sign does not change.
\(\frac{7d}{7}\leq\frac{7}{7}\), so \(d\leq1\).

Answer:

The solution of the inequality \(7(d + 1)-4\leq10\) is \(d\leq1\). On the number - line, we plot a closed circle at \(d = 1\) (because the inequality includes equality, i.e., \(d\) can be equal to 1) and draw a ray to the left of \(d = 1\) to represent all values of \(d\) that satisfy the inequality.