Answer :
To write the sentence as an equation, we start by carefully interpreting each part of the sentence:
1. "274 is equal to..." - This means that one side of the equation is 274.
2. "...[tex]$z$[/tex] subtracted from 163" - This phrase describes a mathematical operation. When you subtract [tex]$z$[/tex] from 163, you are performing the operation [tex]\(163 - z\)[/tex].
Now, putting these understanding together, the complete equation becomes:
[tex]\[ 163 - z = 274 \][/tex]
To solve for [tex]\(z\)[/tex], we need to rearrange the equation. We do this by isolating [tex]\(z\)[/tex] on one side:
1. Start with the equation:
[tex]\[ 163 - z = 274 \][/tex]
2. To solve for [tex]\(z\)[/tex], we need to get [tex]\(z\)[/tex] by itself on one side of the equation. Subtract 163 from both sides of the equation:
[tex]\[ -z = 274 - 163 \][/tex]
3. Calculate [tex]\(274 - 163\)[/tex], which equals 111. So now the equation looks like:
[tex]\[ -z = 111 \][/tex]
4. To find the positive value of [tex]\(z\)[/tex], multiply both sides by -1:
[tex]\[ z = -111 \][/tex]
Therefore, the solution is [tex]\(z = -111\)[/tex].
1. "274 is equal to..." - This means that one side of the equation is 274.
2. "...[tex]$z$[/tex] subtracted from 163" - This phrase describes a mathematical operation. When you subtract [tex]$z$[/tex] from 163, you are performing the operation [tex]\(163 - z\)[/tex].
Now, putting these understanding together, the complete equation becomes:
[tex]\[ 163 - z = 274 \][/tex]
To solve for [tex]\(z\)[/tex], we need to rearrange the equation. We do this by isolating [tex]\(z\)[/tex] on one side:
1. Start with the equation:
[tex]\[ 163 - z = 274 \][/tex]
2. To solve for [tex]\(z\)[/tex], we need to get [tex]\(z\)[/tex] by itself on one side of the equation. Subtract 163 from both sides of the equation:
[tex]\[ -z = 274 - 163 \][/tex]
3. Calculate [tex]\(274 - 163\)[/tex], which equals 111. So now the equation looks like:
[tex]\[ -z = 111 \][/tex]
4. To find the positive value of [tex]\(z\)[/tex], multiply both sides by -1:
[tex]\[ z = -111 \][/tex]
Therefore, the solution is [tex]\(z = -111\)[/tex].
