Question
Evaluate: \( 9 x-57 y-4 z-9 x+52 y+11 z+8 \) when \( x=7, y=4 \) and \( z=6 \) : \( \square \)
Ask by Schultz Wright. in Canada
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of the expression is 30.
Solution
Substitute \( x=7,y=4,z=6 \) into the expression \( 9x-57y-4z-9x+52y+11z+8 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(9x-57y-4z-9x+52y+11z+8\)
- step1: Substitute:
\(9\times 7-57\times 4-4\times 6-9\times 7+52\times 4+11\times 6+8\)
- step2: Multiply the numbers:
\(63-57\times 4-4\times 6-9\times 7+52\times 4+11\times 6+8\)
- step3: Multiply the numbers:
\(63-228-4\times 6-9\times 7+52\times 4+11\times 6+8\)
- step4: Multiply the numbers:
\(63-228-24-9\times 7+52\times 4+11\times 6+8\)
- step5: Multiply the numbers:
\(63-228-24-63+52\times 4+11\times 6+8\)
- step6: Multiply the numbers:
\(63-228-24-63+208+11\times 6+8\)
- step7: Multiply the numbers:
\(63-228-24-63+208+66+8\)
- step8: Calculate:
\(30\)
The value of the expression \(9x-57y-4z-9x+52y+11z+8\) when \(x=7, y=4\) and \(z=6\) is 30.
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Simplify this solution Bonus Knowledge
Let's simplify the expression first: \[ 9x - 57y - 4z - 9x + 52y + 11z + 8 \] Notice that \( 9x \) and \(-9x\) cancel each other out, leaving us with: \[ -57y + 52y - 4z + 11z + 8 \] Now combine the like terms: \[ (-57y + 52y) + (-4z + 11z) + 8 = -5y + 7z + 8 \] Now substitute \( x = 7 \), \( y = 4 \), and \( z = 6 \): \[ -5(4) + 7(6) + 8 \] Calculating each part: \[ -20 + 42 + 8 \] Now, combine these values: \[ -20 + 42 = 22 \] \[ 22 + 8 = 30 \] So the final result is: \[ \boxed{30} \]
