Question

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Solve for x, graph the solution on the numberline.

Answer 1

Answer:

$\tt 5 > 2+\cfrac{x}{3}$

$\tt 2+\cfrac{x}{3} < 5$

(Subtract 2 from both sides):-

• $\tt 2+\cfrac{x}{3}-2 < 5-2$

• $\tt \cfrac{x}{3} < 3$

(Multiply both sides by 3):-

• $\tt \cfrac{3x}{3} < 3\times \:3$

• $\boxed{\underline{\tt x < 9}}$

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$\tt -4+\cfrac{x}{5} < -4$

(Add 4 to both sides):-

• $\tt -4+\cfrac{x}{5}+4 < -4+4$

• $\tt \cfrac{x}{5} < 0$

(Multiply both sides by 5):-

• $\tt \cfrac{5x}{5} < 0\times \:5$

• $\boxed{\underline{\tt x < 0}}$

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$\tt 13 > 3+2x$

(Subtract 3 from both sides):-

• $\tt 3+2x-3 < 13-3$

• $\tt 2x < 10$

(Divide both sides by 2):-

• $\tt \cfrac{2x}{2} < \cfrac{10}{2}$

• $\boxed{\underline{\tt x < 5}}$

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$\tt -2x+4 < 10$

(Subtract 4 from both sides):-

• $\tt -2x < 6$

(Multiply both sides both -1):-

• $\tt -2x\times-1 > 6 \times-1$

• $\tt 2x > -6$

(Divide both sides by 2):-

• $\tt \cfrac{2x}{2} > \cfrac{-6}{2}$

• $\boxed{\underline{\tt x > -3}}$

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(Look at the Attachments)