Problem 91 - Beginning and Intermediate Algebra

Question

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(5 x-2 y+3 a\)

Step-by-Step Solution

Answer

47

Step 1 - Substitute the values

Substitute the given values of the variables into the expression. With the given values: x = 6 y = -4 a = 3 The expression is: 5x - 2y + 3a After substitution, it becomes: 5(6) - 2(-4) + 3(3)

Step 2 - Multiply

Perform the multiplications in the expression: 5(6) = 30 2(-4) = -8 3(3) = 9

Step 3 - Simplify

Simplify the expression by performing the additions and subtractions: 30 - (-8) + 9 Which simplifies to: 30 + 8 + 9 = 47

Key Concepts

Substitution

Substitution is a fundamental concept in algebra. It involves replacing variables in an expression with their given numeric values.

In the exercise, you are asked to evaluate the expression: 5x - 2y + 3a.

To do this, you first need to know the specific values for the variables. Here, they are given as:

x = 6, y = -4, and a = 3.

By substituting these values into the expression, it becomes:
5(6) - 2(-4) + 3(3).

This step is essential because it transforms the algebraic expression with variables into a purely numerical one, which is much easier to work with.

Always ensure you substitute correctly by carefully replacing each variable with its given value.

Multiplication

Once substitution is complete, the next step is to perform multiplication. This involves multiplying the numeric values that replaced the variables.

In our example, after substitution, the expression is:
5(6) - 2(-4) + 3(3).

Here’s the breakdown of each multiplication:

• 5(6) equals 30.
• 2(-4) equals -8 (notice the negative sign).
• 3(3) equals 9.

Multiplication must be done according to the order of operations, which means doing these operations before addition and subtraction.

Accurate multiplication is crucial because any mistake at this stage could lead to a wrong final answer.

Simplification

Simplification is the final step in evaluating the expression. This involves combining like terms and performing basic arithmetic operations to arrive at a single number.

After performing the multiplications from the previous step, our expression is now:
30 - (-8) + 9.

Notice here that subtracting a negative number is the same as adding the absolute value of that number. So, 30 - (-8) becomes 30 + 8.

We now add the numbers together:

• 30 + 8 equals 38.
• Then, add 9 to 38, which gives us 47.

Simplification combines all parts of the expression into one final result, which, in this case, is 47.

This step ensures the expression is fully evaluated and simplified to its most understandable form.