Question

Write and solve an inequality to determine the values of x for which 4 - 3x is nogreater than 7 - X.

Answer 1

Let's write the inequality to determine the values of x for which 4 - 3x is no greater than 7-x.

Since 4 - 3x is no greater than 7-x, it means 4-3x is less than or equal to 7-x.

Thus, the inequality sign we are to use is that of "less than or equal to".

We have the inequality below:

`4-3x\leq7-x`

Let's solve for x.

Subtract 4 from both sides of the inequality:

`\begin{gathered} -4+4-3x\leq-4+7-x \\ \\ -3x\leq3-x \end{gathered}`

Add x to both sides of the inequality:

`\begin{gathered} -3x+x\leq3-x+x \\ \\ -2x\leq3 \end{gathered}`

Divide both sides by -2:

`\begin{gathered} (-2x)/(-2)\leq(3)/(-2) \\ \\ x\ge-1.5 \end{gathered}`

Therefore, the vaule of x must be greater or equal to -1.5

ANSWER:

`x\ge-1.5`