Checking Solutions to Equations

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

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

• Multiply 3 by 4 and check if it equals 10.

• Add 3 and 4 to see if it equals 12.

• Subtract 4 from 12 to find the value of x.

What is the solution to the equation 2x + 3 = 13?

• x = 4

• x = 5

• x = 6

• x = 7

What is an equation?

• A mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

• A formula used to calculate the area of a circle.

• A type of graph that represents data points in a coordinate system.

• A statement that describes a relationship between two quantities without using variables.

Is x=7 a solution to the equation 5x - 10 = 25?

• Yes, substituting x=7 gives 5(7) - 10 = 25, which is true.

• No, substituting x=7 gives 5(7) - 10 = 20, which is false.

• Yes, substituting x=7 gives 5(7) - 10 = 30, which is true.

• No, substituting x=7 gives 5(7) - 10 = 15, which is false.

Is x=5 a solution to the equation 2x + 3 = 13?

• Yes, substituting x=5 gives 2(5) + 3 = 13, which is true.

• No, substituting x=5 gives 2(5) + 3 = 10, which is false.

• Yes, substituting x=5 gives 2(5) + 3 = 15, which is true.

• No, substituting x=5 gives 2(5) + 3 = 8, which is false.

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

• It means to ignore the proposed solution and find a new one.

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

• It requires rewriting the equation in a different form.

• It is the process of guessing the solution without any calculations.

What is the importance of checking solutions in equations?

• It helps to find new solutions.

• It ensures that the proposed values satisfy the original equation, confirming their validity.

• It makes the equations easier to solve.

• It allows for the elimination of variables.

What is a variable in an equation?

• A variable is a constant value that does not change.

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

• A variable is a type of equation that has no solution.

• A variable is a number that can be calculated from other numbers.

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

• Yes, substituting z=10 gives 15 = 15.

• No, substituting z=10 gives 5 = 15.

• Yes, substituting z=10 gives 20 = 15.

• No, substituting z=10 gives 15 = 10.

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

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

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

• 3. Distribute: 3y + 3 = 4y - 5; Rearrange: 3 + 5 = 4y + 3y; Combine: 8 = 7y.

• 4. Distribute: 3y + 3 = 4y - 5; Rearrange: 3 - 5 = 4y + 3y; Combine: -2 = 7y.