Exercise 43 Page 198

To solve the inequality, we have to isolate x. By distributing - 3 on the left-hand side and using inverse operations, we can isolate the variable.

- 3(4x+8)+1≥- 23

Distr

Distribute - 3

- 12x-24+1≥- 23

AddTerms

Add terms

- 12x-23≥- 23

AddIneq

LHS+23≥RHS+23

- 12x≥ 0

DivNegIneq

Divide by - 12 and flip inequality sign

x≤ 0

Now we can use the result to form a solution set in set-builder notation. { x | x≤0 } This can be read as all values of x such that x is less than or equal to 0.