Question

1. mp structure use the graph to solve |2x + 4| = |x - 1|. check your solutions.

Explanation:

Step1: Identify intersection points

The solutions are the x-coordinates of the points where $y=|2x+4|$ (red graph) and $y=|x-1|$ (blue graph) intersect. From the graph, the intersection points have x-values $x=-1$ and $x=-5$.

Step2: Verify $x=-1$

Substitute $x=-1$ into the original equation:
Left side: $|2(-1)+4|=|-2+4|=|2|=2$
Right side: $|-1-1|=|-2|=2$
Both sides are equal, so $x=-1$ is valid.

Step3: Verify $x=-5$

Substitute $x=-5$ into the original equation:
Left side: $|2(-5)+4|=|-10+4|=|-6|=6$
Right side: $|-5-1|=|-6|=6$
Both sides are equal, so $x=-5$ is valid.

Answer:

The solutions are $x=-5$ and $x=-1$.