Question

Which graph represents the solutions to the inequality |2x - 6| < 4?

number line with a closed circle on 1, shading to the left and a closed circle on 5, shading to the right
number line with a closed circle on 1, shading to the right and a closed circle on 5, shading to the left
number line with an open circle on 1, shading to the left and an open circle on 5, shading to the right
number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left

Answer 1

@hero

Answer 2

the vertical lines around 2x-6 means the absolute value of 2x - 6, whether the expression is negative or positive
this gives us 2 inequalities:-
2x - 6 < 4 and 2x - 6 > -4

can you solve these?

Answer 3

First of all, we can eliminate two choices because the inequality is simply a "less than" sign. This means we don't include the very last number, which means an open circle is needed. I suggest temporarily changing the sign to an equal sign to solve for the highest and lowest x values since the answer is everything in between them (and not the end points as just discussed).

Answer 4

i believe the answer is d @welshfella @nuttyliaczar

Answer 5

you solved the inequalities then?

Answer 6

Also a good practice is to see what the different equations are for each graph. There is one tiny difference between the equations for graphs C and D, do you know what it is? (And yes you are correct)

Answer 7

ok may you busy help me with another ? @nuttyliaczar @welshfella