Question

Evaluate each expression if $d=4$,$f=3$ and $g=12$.

$5d+\left(6f-g\right)$

Short answer

The value of the expression $\mathbf{5}\mathit{d}\mathbf{+}\left(6f-g\right)$is 26.

Step-by-step solution

Step 1. Evaluation of algebraic expression.

To evaluate an expression with different operations, an order needs to be followed. The order is first, we open the parenthesis, then solve exponents, then multiply and/or divide and then finally add and/or subtract.

Step 2. Replace the variables.

Substitute 4 for d, 3 for f, and 12 for g into the equation $5d+\left(6f-g\right)$.

$5d+\left(6f-g\right)=5\cdot 4+\left(6\cdot 3-12\right)$

Step 3. Apply the order of operations.

As per the order of operations, first, evaluate the expressions inside the bracket.

$\begin{array}{l}5d+\left(6f-g\right)=5\cdot 4+\left(18-12\right)\\ =5\cdot 4+6\\ =20+6\\ =26\end{array}$

Therefore, the expression is equal to 26.