Question

algebra 1 eoc 2024 released items
4
a compound inequality is shown.
2x - 1 ≤ 3 or 1/2x + 4 > 7
solve and graph the inequality.
5
an inequality is shown.
-3x + 7 ≥ -x - 5
what is the solution set for x?
6
what is the sum of (2x³ + 4x) and (3x³ + 5x)?
page 3 of 23
algebra 1 eoc 2024 released items
7
a system of equations is shown.
y = 2x + 2
2x + 5y = 19

Explanation:

Question 4

Step1: Solve the first - inequality

Solve $2x - 1\leq3$. Add 1 to both sides: $2x\leq3 + 1$, so $2x\leq4$. Divide both sides by 2: $x\leq2$.

Step2: Solve the second - inequality

Solve $\frac{1}{2}x+4 > 7$. Subtract 4 from both sides: $\frac{1}{2}x>7 - 4$, so $\frac{1}{2}x>3$. Multiply both sides by 2: $x > 6$.

Step3: Graph the solution

The solution of the compound inequality $2x - 1\leq3$ or $\frac{1}{2}x + 4>7$ is $x\leq2$ or $x > 6$. On a number - line, we have a closed circle at $x = 2$ (since $x$ can equal 2 for the first inequality) and an arrow to the left for $x\leq2$, and an open circle at $x = 6$ (since $x$ cannot equal 6 for the second inequality) and an arrow to the right for $x>6$.

Step1: Add $3x$ to both sides

Starting with $-3x + 7\geq -x - 5$, we get $7\geq -x+3x - 5$, which simplifies to $7\geq2x - 5$.

Step2: Add 5 to both sides

$7 + 5\geq2x$, so $12\geq2x$.

Step3: Divide both sides by 2

$x\leq6$.

Step1: Add the like - terms

$(2x^{3}+4x)+(3x^{3}+5x)=(2x^{3}+3x^{3})+(4x + 5x)$.

Step2: Combine the like - terms

$2x^{3}+3x^{3}=5x^{3}$ and $4x + 5x = 9x$. So the sum is $5x^{3}+9x$.

Answer:

The solution is $x\leq2$ or $x > 6$.

Question 5