Sure! Let's solve the inequality step by step:
Given inequality:
[tex]\[ 7(3e + 4) - (5e - 7) \leq 6 \][/tex]
Step 1: Distribute and simplify the expressions
First, distribute the 7 inside the parentheses:
[tex]\[ 7 \cdot 3e + 7 \cdot 4 = 21e + 28 \][/tex]
So now the inequality becomes:
[tex]\[ 21e + 28 - (5e - 7) \leq 6 \][/tex]
Next, distribute the negative sign:
[tex]\[ 21e + 28 - 5e + 7 \leq 6 \][/tex]
Combine like terms:
[tex]\[ (21e - 5e) + (28 + 7) \leq 6 \][/tex]
[tex]\[ 16e + 35 \leq 6 \][/tex]
Step 2: Isolate the variable (e)
Subtract 35 from both sides of the inequality to isolate the term with the variable [tex]\(e\)[/tex]:
[tex]\[ 16e + 35 - 35 \leq 6 - 35 \][/tex]
[tex]\[ 16e \leq -29 \][/tex]
Step 3: Solve for [tex]\(e\)[/tex]
Divide both sides by 16 to solve for [tex]\(e\)[/tex]:
[tex]\[ e \leq \frac{-29}{16} \][/tex]
Thus, the solution to the inequality is:
[tex]\[ e \leq -\frac{29}{16} \][/tex]
Hence, the final answer is:
[tex]\[ (-\infty < e) \ \text{and} \ (e \leq -\frac{29}{16}) \][/tex]
