Solve 7x + 1 < 4(x - 2).
{x | x < 3}
{x | x > 3}
{x | x > -3}
{x | x < -3}

The general approach to solving any such inequality is to get the variable by itself on one side of the relationship symbol. The instructions for this can vary, but here is a set of instructions that will always work.

1. Subtract the expression on the right side of the relationship symbol.

... 7x + 1 < 4(x - 2) . . . . starting inequality

... 7x +1 - 4(x -2) < 0 . . . after step 1

2. Eliminate parentheses and collect terms.

... 7x +1 -4x +8 < 0

... 3x +9 < 0 . . . . . . . . . after step 2

3. Divide by the coefficient of the variable. Here, divide by 3. If the coefficient of the variable is negative, also reverse the relationship symbol (≥ becomes ≤, for example).

... x + 3 < 0 . . . . . . . . . we divided by 3

4. Add the opposite of the constant, if any.

... x < -3 . . . . . . . . . . . . after adding -3

This solution matches your 4th selection:

... {x | x < -3}

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: