Checking Solutions to Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean to check a solution to an equation?

Back

Checking a solution involves substituting the proposed solution back into the original equation to see if both sides are equal.

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by letters like x or y, that stands for an unknown value in an equation.

Front

How do you solve the equation 3(y + 1) = 4y - 5?

Back

1. Distribute: 3y + 3 = 4y - 5; 2. Rearrange: 3 + 5 = 4y - 3y; 3. Combine: 8 = y.

Front

Is y=8 a solution to the equation 3(y + 1) = 4y - 5?

Back

Yes, substituting y=8 gives 3(8 + 1) = 4(8) - 5, which simplifies to 27 = 27.

Front

What is the solution to the equation 3x = 12?

Back

x = 4, because dividing both sides by 3 gives x = 12/3.

Front

How do you check if x=4 is a solution to 3x=12?

Back

Substitute 4 into the equation: 3(4) = 12, which is true.

Front

What does it mean if a value is a solution to an equation?

Back

It means that when the value is substituted into the equation, both sides of the equation are equal.

Front

Is 10 a solution to the equation 2z - 5 = 4z - 25?

Back

Yes, substituting z=10 gives 2(10) - 5 = 4(10) - 25, which simplifies to 15 = 15.

Front

How do you solve the equation 5x - 10 = 25?

Back

1. Add 10 to both sides: 5x = 35; 2. Divide by 5: x = 7.