DC CAPE Algebra I Reasoning with Equations and Inequalities. Practice it free.

This domain measures students' ability to solve equations and inequalities and interpret their solutions. This Algebra I reporting domain maps to 21 practice skills and 8 representative questions from the playable bank.

Algebra IReasoning with Equations and Inequalities21 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

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playhard

If $\dfrac{5x - 2y}{x + 3y} = \dfrac{2}{3}$ , then $\dfrac{x}{y}=$

Cross-multiply to clear the fraction: $3(5x - 2y) = 2(x + 3y)$ , so $15x - 6y = 2x + 6y$ . Collect like terms to get $13x = 12y$ . Divide both sides by $y$ , then by $13$ , to obtain $\dfrac{x}{y} = \dfrac{12}{13}\textsf{.}$

Practice playmedium

If $\dfrac{(x+2)(x-8)}{x+2} = 5$ and $x \neq -2\textsf{,}$ what is the value of $x\textsf{?}$

For $x \neq -2$ , the factor $x+2$ cancels, giving $x-8 = 5$ , so $x = 13\textsf{.}$

Practice playeasy

How many distinct real roots does $x^{2} - 10x + 25 = 0$ have?

Here $a = 1$ , $b = -10$ , and $c = 25$ . Substituting into $b^{2} - 4ac$ gives $(-10)^{2} - 4(1)(25) = 0\textsf{,}$ so there is exactly $1$ distinct real root.

Practice playeasy

What is the discriminant of $2x^{2} - 7x + 3 = 0$ ?

Here $a = 2$ , $b = -7$ , and $c = 3$ . Substituting into $b^{2} - 4ac$ gives $(-7)^{2} - 4(2)(3) = 49 - 24 = 25$ .

Practice playmedium

How many distinct real solutions does the equation $2x^{2} - 5x - 3 = 0$ have?

The quadratic factors as $(2x + 1)(x - 3) = 0\textsf{.}$ Then $2x + 1 = 0$ or $x - 3 = 0\textsf{,}$ so $x = -\dfrac{1}{2}$ or $x = 3\textsf{.}$ There are $2$ distinct real solutions.

Practice playeasy

What is the positive solution of $4x^{2} - 9x - 9 = 0\textsf{?}$

The quadratic factors as $(4x + 3)(x - 3) = 0\textsf{.}$ By the zero-product property, $4x + 3 = 0$ or $x - 3 = 0\textsf{,}$ so $x = -\dfrac{3}{4}$ or $x = 3\textsf{.}$ The positive solution is $3\textsf{.}$

Practice playeasy

$|x + 16| = 27$

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

The equation means $x + 16 = 27$ or $x + 16 = -27$ . So $x = 11$ or $x = -43$ . Both solutions are $-43$ and $11\textsf{.}$

Practice playmedium

If $|x - 2| = 11$ , what is the positive value of $2x$ ?

Either $x - 2 = 11$ , giving $x = 13$ and $2x = 26$ , or $x - 2 = -11$ , giving $x = -9$ and $2x = -18$ . The positive value of $2x$ is $26\textsf{.}$