HS Math Solutions - Algebra: Equations

Algebra: Equations

Contents (5 topics • 46 videos)

Solving One-Step Equations (11 videos)

Solving Two-Step Equations (8 videos)

Solving Multi-Step Equations and Algebraic Proofs (13 videos)

Equations with No Solution or Infinite Solutions (5 videos)

Solving Literal Equations (9 videos)

Solving One-Step Equations

Introduction Videos

Solving One-Step Equations Using Addition and Subtraction

Solving One-Step Equations Using Multiplication and Division

Theorems and Definitions

Properties of Equality for Solving Equations

Name of Property

Verbal Description

Algebraic Description

Addition Property of Equality

Adding a value to one side of an equation requires adding that value to the other side of the equation to keep the two sides equal.

If \( a=b \), then
\( a+c=b+c \).

Subtraction Property of Equality

Subtracting a value from one side of an equation requires subtracting that value from the other side of the equation to keep the two sides equal.

If \( a=b \), then
\( a-c=b-c \).

Multiplication Property of Equality

Multiplying one side of an equation by a value requires multiplying the other side of the equation by the same value to keep the two sides equal.

If \( a=b \), then
\( a \cdot c=b \cdot c \).

Division Property of Equality

Dividing one side of an equation by a value requires dividing the other side of the equation by the same value to keep the two sides equal.

If \( a=b \), then
\( \frac{a}{c} = \frac{b}{c} \).

Symmetric Property of Equality

If two sides of an equation are equal, then they can be exchanged for one another.

If \( a=x \), then
\( x=a \).

Video Practice Problems Playlist on YouTube

Solve.
\[ x-17=-8 \]

Solve.
\[ y+13=5 \]

Solve.
\[ -8=n+(-3) \]

Solve.
\[ \frac{3}{4}=-\frac{6}{5}+b \]

Solve.
\[ -3m=21 \]

Solve.
\[ \frac{n}{-4}=-8 \]

Solve.
\[ \frac{3}{14}x=-6 \]

Solve.
\[ -\frac{5}{2}x=-\frac{3}{4} \]

Solve.
\[ -0.09k=8.1 \]

Documents

Practice Problems (.PDF)

Solving Two-Step Equations

Introduction Videos

Solving Two-Step Equations

Video Practice Problems Playlist on YouTube

Solve.
\[ 4n+3=15 \]

Solve.
\[ -w+6=2 \]

Solve.
\[ 15-8m=79 \]

Solve.
\[ \frac{2}{3}k-\frac{4}{5}=\frac{8}{15} \]

Solve.
\[ -3=\frac{p-5}{4} \]

Solve and evaluate.
\[ \frac{g-7}{-2}=5 \text{; } \quad g^2-5 \]

Solve and evaluate.
\[ \frac{3}{4}=\frac{1}{2}-\frac{3}{8}y \text{; } \quad 1-3y \]

Documents

Practice Problems (.PDF)

Solving Multi-Step Equations

Introduction Videos

Solving Multi-Step Equations

Solving Equations with an Algebraic Proof

Solving Proportions with Monomials and Binomials

Video Practice Problems Playlist on YouTube

Solve.
\[ 4d-11=7d+4 \] Solve.
\[ 2c+4=4(5-c)+2 \]

Solve.
\[ 3=\frac{6-7a}{-5} \] Solve.
\[ 2(3y+4)-2=-3+3(y+2) \]

(Algebraic Proof)
Solve. Justify each step.
\[ 7a-17=1+4a \] (Algebraic Proof)
Solve. Justify each step.
\[ 3m-10=2(4m-5) \]

Solve.
\[ \frac{x-4}{6} = \frac{4}{3} \] Solve.
\[ \frac{10.5}{14} = \frac{3}{x-3} \] Solve.
\[ \frac{6}{-5x} = \frac{15}{17-4x} \] Solve.
\[ \frac{x+7}{18} = \frac{x+4}{12} \]

Equations with No Solution or Infinite Solutions

Introduction Videos

Equations with No Solution or Infinite Solutions

Theorems and Definitions

Equations with No Solution or Infinite Solutions No Solution When solving an equation, if every variable cancels and the remaining numeric statement is false, then the equation has "No Solution."

Infinite Solutions When solving an equation, if every variable cancels and the remaining numeric statement is true, then the equation has an infinite number of solutions, or its solution is said to be "All Real Numbers."

Video Practice Problems Playlist on YouTube

Solve.
\[ 2a+3(a+2)-3=5(a-1)+3 \] Solve.
\[ 7k-2(3k-1)=2(6+k)-k \]

Solve.
\[ -6(1-2y)=4(3y-1)-2 \] Solve.
\[ 3(7x+2)-5x=8(2x+1)-2 \]

Solving Literal Equations

Introduction Videos

Solving Literal Equations

Solving Literal Equations that Requires Factoring (GCF)

Video Practice Problems Playlist on YouTube

Solve for \( R \).
\[ I=PRT \] Solve for \( m \).
\[ y=mx+b \] Solve for \( b \).
\[ A=\frac{1}{2}bh \] Solve for \( a \).
\[ \frac{5a-3b}{4}=6b+2a-3 \]

Solve for \( m \).
\[ 2mn+3=n-5m \] Solve for \( a \).
\[ 5a-c=b(3a+2) \] Solve for \( y \).
\[ \frac{1}{12}(9y-8x)=-2(2+xy)+\frac{1}{2}y \]