Georgia Milestones Algebra II Reasoning with Equations and Inequalities. Practice it free.

Students solve equations and inequalities and analyze systems and algebraic structure. This Algebra II reporting domain maps to 21 practice skills and 8 representative questions from the playable bank.

Algebra II21 mapped skills

What the test measures

Reasoning with Equations and Inequalities skills

Understand solving equations as a process of reasoning and explain the reasoning
Solve equations and inequalities in one variable
Solve systems of equations
Represent and solve equations and inequalities graphically

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

Official sources

Georgia Department of Education

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

$|x + 8| = 21$

Which of the following gives both solutions to the given equation?

The equation means $x + 8 = 21$ or $x + 8 = -21$ . So $x = 13$ or $x = -29$ . Both solutions are $-29$ and $13\textsf{.}$

Practice playeasy

If $|2x + 10| = 26$ , what is the positive value of $x + 5$ ?

Rewrite $|2x + 10| = |2(x + 5)| = |2|\,|x + 5| = 2|x + 5|$ . Since $2|x + 5| = 26$ , divide by $2$ to get $|x + 5| = 13$ . The expression $x + 5$ equals $13$ or $-13$ ; the positive value is $13\textsf{.}$

Practice playeasy

How many distinct real roots does $x^{2} - 25 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = -25$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(-25) = 100\textsf{,}$ so there are $2$ distinct real roots.

Practice playeasy

How many distinct real solutions does $x^{2} + 6x + 9 = 0$ have?

Here $a = 1$ , $b = 6$ , and $c = 9$ . Substituting into $b^{2} - 4ac$ gives $6^{2} - 4(1)(9) = 0$ , so there is exactly $1$ distinct real solution.

Practice playeasy

If $6x = 54$ , what is the value of $x + 7$ ?

Divide both sides by $6$ : $x = 9$ . Then $x + 7 = 9 + 7 = 16\textsf{.}$

Practice playeasy

Solve for $x$ : $x - 3 > 4$ . The solution is $x > k$ . What is the value of $k$ ?

Add 3 to both sides: $x > 7$ , so $k = 7$ .

Practice playeasy

$\begin{cases} y > 3x - 5 \\ y \le x + 4 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 2$ , which of the following could be a value of $y$ ?

Substitute $x = 2$ . From $y > 3x - 5$ , $y > 1$ . From $y \le x + 4$ , $y \le 6$ . The value $y = 4$ satisfies $1 < 4 \le 6$ .

Practice playmedium

The line $y=x-4$ and the parabola $y=-x^{2}+5x-4$ intersect at one of these $(x,y)$ points. Which one?

Set the expressions equal: $x-4=-x^{2}+5x-4$ , so $0=-x^{2}+4x$ . Then $0=-x(x-4)$ , and $x=0$ or $x=4$ . For $x=4$ , $y=4-4=0$ , so one intersection point is $(4,0)\textsf{.}$