ccss.hsa-sse.a.1.q.a1.hdc.2 - Graph the solutions to the inequality 7x-3y \leq 21

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

Here is how we graph or find the solution to an inequality

STEP 1:Write this inequality in the standard form by isolating the y variable

-3y \leq 21 - 7x

Divide the inequality with -3 on either side, doing so will flip the inequality from \leq to \geq,

and we get

\frac{-3y}{-3} \geq \frac{21}{-3} - \frac{7x}{-3}

y \geq -7 + \frac{7}{3}x

STEP 3: Find the solutions to the inequality, by replacing the above inequality with an equality and finding the x-and the y-intercepts.

y = -7 + \frac{7}{3}x

Plug in x = 0 to get y = -7 and then plug in y = 0 to get x = 3.

So, (0,-7) and (3,0) are solutions to the inequality y \geq -7 + \frac{7}{3}x

STEP 4: Plot these two points (0,-7) and (0,3) on the graph and join them with a solid line.

Recall that we have a solid line when there is an = to in the inequality.

STEP 5: Since we have a \geq inequality now , the region above the line is shaded.

Skills to recall:

What is an inequality

How to graph an inequality