Which inequality describes all the solutions to -3(4 – x) + 6 < 9 – 2x?

Answer:

To do inequalities, you just need to solve the equality and then figure out what side (higher or lower) the solution is on and put in the appropriate greater-than, less-than, greater-than-or-equal-to or less-than-or-equal-to sign.

Think about the equality for this one. What equation could we right for the average number of words per week that would put Trevor right at 50,000 after 5 weeks.

If we call the number of words per week, w, we would have

w = [an expression]   (You find the expression using the number of words he has to write and how many weeks he has.)

Now think about the inequality. Trevor wants to finish in five weeks or less. So as long as he writes at least this number of words per week, he'll make it. That means we want a greater-than-or-equal to sign:

w ≥ [your expression]

Step-by-step explanation:

The inequality which describes all the solutions to the inequality is

x < 3

Given the inequality expression given as -3(4 – x) + 6 < 9 – 2x, we need to find the solution to the system of inequality as shown:

[tex]-3(4 -x) + 6 < 9 - 2x[/tex]

Expand the bracket

[tex]-3(4 -x) + 6 < 9 - 2x\\-12+3x+6<9-2x\\3x-6<9-2x\\3x+2x<9+6\\5x<15\\x<15/5\\x<3[/tex]

Hence the inequality which describes all the solutions to the inequality is

x < 3

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