The correct solution graph to the inequalities are
[tex]4(9x-18)>3(8x+12)[/tex] → C
[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex] → A
[tex]1.6(x+8)\geq 38.4[/tex] → B
(NOTE: The graphs are labelled A, B and C from left to right)
For the first inequality,
[tex]4(9x-18)>3(8x+12)[/tex]
First, clear the brackets,
[tex]36x-72>24x+36[/tex]
Then, collect like terms
[tex]36x-24x>36+72\\12x >108[/tex]
Now divide both sides by 12
[tex]\frac{12x}{12} > \frac{108}{12}[/tex]
∴ [tex]x > 9[/tex]
For the second inequality
[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex]
First, clear the fraction by multiplying both sides by 3
[tex]3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)[/tex]
[tex]-1(12x+6) \geq -6x +42[/tex]
Now, open the bracket
[tex]-12x-6 \geq -6x +42[/tex]
Collect like terms
[tex]-6 -42\geq -6x +12x[/tex]
[tex]-48\geq 6x[/tex]
Divide both sides by 6
[tex]\frac{-48}{6} \geq \frac{6x}{6}[/tex]
[tex]-8\geq x[/tex]
∴ [tex]x\leq -8[/tex]
For the third inequality,
[tex]1.6(x+8)\geq 38.4[/tex]
First, clear the brackets
[tex]1.6x + 12.8\geq 38.4[/tex]
Collect likes terms
[tex]1.6x \geq 38.4-12.8[/tex]
[tex]1.6x \geq 25.6[/tex]
Divide both sides by 1.6
[tex]\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}[/tex]
∴ [tex]x \geq 16[/tex]
Let the graphs be A, B and C from left to right
The first graph (A) shows [tex]x\leq -8[/tex] and this matches the 2nd inequality
The second graph (B) shows [tex]x \geq 16[/tex] and this matches the 3rd inequality
The third graph (C) shows [tex]x > 9[/tex] and this matches the 1st inequality
Hence, the correct solution graph to the inequalities are
[tex]4(9x-18)>3(8x+12)[/tex] → C
[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex] → A
[tex]1.6(x+8)\geq 38.4[/tex] → B
Learn more here: https://brainly.com/question/17448505
