Problem 74 - Algebra 1

Question

Check whether the given number is a solution of the equation. $$x+5=11 ; 7$$

Step-by-Step Solution

Answer

7 is not a solution for the equation \(x+5=11\), because \(7+5\) equals to \(12\), not \(11\).

Step 1: Substitute the given value

Substitute the given number into the equation in place of x. This would give \(7+5\).

Step 2: Perform the operation

Perform the operation on the left side of the equation which would yield \(12\).

Step 3: Compare the results

Compare \(12\) to the right side of the equation which is \(11\).

Key Concepts

Equation Solving

In math, solving an equation means we are trying to find out what number makes the equation true. Imagine an equation like a balance scale. Each side should weigh the same to make it balanced or true. Given the equation from our exercise, which is \( x + 5 = 11 \), we want to find a number for \( x \) so that when we add 5, the total will be 11. To solve, we simply do the mathematics to check if our chosen number fits perfectly into the equation, making both sides equal.

Substitution Method

The substitution method is a key trick in algebra that makes checking solutions easier.
In our case, we have a number, 7, and we are asked to check if it solves the equation \( x + 5 = 11 \). This means, instead of \( x \), we plug in 7 wherever \( x \) appears in the equation:

• Begin with the original equation: \( x + 5 = 11 \).
• Substitute the number 7 in place of \( x \).
• This gives us \( 7 + 5 \).

This method is wonderfully straightforward because it's simply about replacing a variable with a given number and then calculating to see if the equation holds true.

Comparing Expressions

Once we substitute the number into our equation, the next task is comparing.
Now, perform the math.
With our substituted expression, \( 7 + 5 \), we calculate it to find the result is 12. Comparing mean we look at whether 12 matches the right-hand side of our original equation, which is 11. Since 12 is not equal to 11, 7 is not a solution for the equation.

• If both sides equal after substitution, the number is a solution.
• If they do not, as in this case, it is not.

This step shows how important it is to check both sides—it's like double-checking your math homework to make sure it’s correct!