91Ó°ÊÓ

The substitution method is a handy technique in algebra used to replace a variable with its actual value. Imagine you have a placeholder in a sentence, just like a variable in math. When given a specific number to replace the placeholder, you perform the substitution. In our exercise, the expression given was \(-5x + 20\), and we were told that \(x = 4\). By substituting 4 in place of \(x\), the expression changes. So, \(-5 \times x + 20\) turns to \(-5 \times 4 + 20\). This step is vital as it sets the stage for further calculations. Substitution ensures every part of the expression reflects the true value it intends to represent. When you follow this method, always double-check: replace only the variable provided and maintain other numbers in the expression.

Evaluating expressions involves calculating their values after substitution. You see an expression like a puzzle. With all pieces in place, it's time to find the solution. Once substitution is done, it’s important to carry out arithmetic operations like multiplication, division, addition, or subtraction. Simply follow the order of operations—anything within parentheses first, then exponents, followed by multiplication and division, and finally addition and subtraction. In our case, after substituting \(x = 4\), we had \(-5(4) + 20\). Multiplying yields \(-20\). Next in line was addition: \(-20 + 20\). The expression evaluated to 0. Each step depends on proper arithmetic skills. Staying methodical and checking your work ensures accuracy in your answer.

Simplifying expressions means breaking them down to their most basic form. After evaluation, your goal is to express it clearly and directly.In the expression \(-20 + 20\), when added, the opposite numbers cancel out, leaving zero. This is simplification at work. You start with one form and, through calculations, find the simplest version. Simplification makes expressions easier to understand and work with. This step reduces complexity and highlights the essential value, which can prove handy in solving larger problems or equations. Remember, ensure every term is accounted for, and common errors like ignoring negative signs are avoided in your simplification process.