Question

solve for $x$ and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution ($\varnothing$), leave the number line blank.
$2x + 7 < 9$ and $2x + 7 < 21$
answer
< > ≤ ≥ or $\varnothing$ $\mathbb{r}$
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
submit answer

Explanation:

Step1: Solve the first inequality

Subtract 7 from both sides of $2x + 7<9$.
$2x+7 - 7<9 - 7$
$2x<2$
Then divide both sides by 2: $x < 1$.

Step2: Solve the second inequality

Subtract 7 from both sides of $2x + 7<21$.
$2x+7 - 7<21 - 7$
$2x<14$
Then divide both sides by 2: $x < 7$.

Step3: Find the intersection

Since we have $x < 1$ and $x < 7$, the intersection of these two inequalities is $x < 1$ (because if $x$ is less than 1, it is also less than 7).

Answer:

Inequality Notation: $x < 1$
Number Line: Mark an open - circle at 1 and shade the line to the left of 1.