What does the letter 'a' represent in the standard form of a linear equation?
Coefficient
Match the term with its role in a linear equation:
Coefficient ↔️ Multiplies the variable
Variable ↔️ Represents an unknown value
Constant ↔️ Added to the variable term
Total value ↔️ Represents the constant on the other side
In solving a linear equation, you divide both sides by the coefficient of the variable
When do you reverse the inequality sign in solving inequalities?
When dividing by a negative number
Adding or subtracting the same number to both sides of an inequality does not change the inequality
Multiplying or dividing both sides of an inequality by a positive number does not change the inequality sign
What happens to an inequality sign when both sides are multiplied by a negative number?
It reverses
What operation reverses the inequality sign?
Multiplying by a negative
Steps to solve a linear equation with one unknown
1️⃣ Isolate the variable
2️⃣ Simplify the equation
3️⃣ Divide by the coefficient
The key difference between inequalities and equations is that multiplication or division by a negative number requires you to reverse the inequality sign
Multiplying both sides of an inequality by a negative number reverses the inequality sign
When solving equations with fractions, it may be necessary to find a common denominator
To solve equations with brackets, the first step is to expand the brackets using the distributive property
Match the term in a linear equation with its role:
a ↔️ Coefficient
x ↔️ Variable
b ↔️ Constant added to variable
c ↔️ Total value on the other side
The constant 'b' in a linear equation is added to or subtracted from the variable term
True
The coefficient 'a' in a linear equation multiplies the variable
Steps to solve a linear equation with one unknown
1️⃣ Isolate the variable
2️⃣ Simplify like terms
3️⃣ Divide by the coefficient
To simplify an equation, combine like terms on each side.
Dividing both sides of 3x = 9 by 3 gives x = 3
Multiplying both sides of an inequality by a positive number does not change the sign
Adding the same number to both sides of an inequality changes the inequality sign.
False
Steps for solving equations and inequalities with fractions
1️⃣ Isolate the variable
2️⃣ Simplify like terms
3️⃣ Reduce fractions
4️⃣ Divide by fractional coefficient
When dividing by a fractional coefficient in an equation, you must invert the fraction.
Steps for solving equations and inequalities with brackets
1️⃣ Expand the brackets
2️⃣ Isolate the variable
3️⃣ Combine like terms
4️⃣ Solve for the variable
5️⃣ Reverse the inequality sign if necessary
Match the action with the example:
Expand Brackets ↔️ 3(x + 2) = 3x + 6
Isolate Variable ↔️ 3x = 6 - 6
Combine Like Terms ↔️ 3x = 0
Solve for Variable ↔️ x = 0 / 3 = 0
What is the solution for x in the equation 3(x + 2) = 6?
x = 0
When checking if x = 2 is a solution to 3x + 1 = 7, the evaluation shows that 7 = 7.
True
Checking if x = 2 is a solution to 3x + 1 = 7 results in 7 = 7, which means x = 2 is a correct solution.
True
In the quadratic equation 3x^2 - 2x + 4 = 0, the value of a is 3.
True
In the linear equation 3x + 5 = 14, the coefficient a is 3.
True
Multiplying both sides of an inequality by -1 reverses the inequality sign.
True
What is the first step in solving an inequality with one unknown?
Isolate the variable
What happens to the inequality sign when multiplying both sides by a negative number?
It reverses
What is the first step in solving the inequality `(2/3)x + 1 ≤ 5`?
Subtract 1 from both sides
You must reverse the inequality sign when multiplying by a positive number.
False
A linear equation in the standard form is written as ax + b = c
The constant term 'b' in a linear equation does not depend on the variable
To solve a linear equation, you must isolate the variable using inverse operations.
True
Order the steps to solve a linear equation with one unknown:
1️⃣ Isolate the variable
2️⃣ Simplify like terms
3️⃣ Divide by the coefficient
If you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign