Write an algebraic expression for the word phrase.
the difference between a number q and 8
Solve each equation. Show all steps.
x+5=−2
3a+2 − 5a=−14
n5=13
Simplify the expression. Show all steps
53+(−12)+(−4t)
Solve the literal equation for x. Show all steps.
4(x − b)=x
Algebraic expressions:
1) q - 8
2) x + 5 = -2
3) 3a + 2 - 5a = -14
4) n * 5 = 13
5) 53 + (-12) + (-4t)
Solving equations:
2) x + 5 = -2
Subtract 5 from both sides: x = -7
3) 3a + 2 - 5a = -14
Combine like terms: -2a + 2 = -14
Subtract 2 from both sides: -2a = -16
Divide by -2: a = 8
4) n * 5 = 13
Divide both sides by 5: n = 2.6
Simplifying expression:
5) 53 + (-12) + (-4t)
Combine like terms: 41 + (-4t)
Simplify further: -4t + 41
Solving literal equation:
6) 4(x - b) = x
Distribute 4: 4x - 4b = x
Subtract 4x from both sides: -4b = -3x
Divide by -3: 4b = 3x
Divide by 3: b = 3/4x