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Solve for x in the following algebra problems: a) x+7=15, b) -3x=-6, c) 9x−7=11, d) x/4=-5, e) -x/3+1=3, f) (3x-1)/2=2, g) x−8=19

Mathematics

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Here are the solutions to the algebra problems:

Part a· 2 steps

Solve for xx

x+7=15x+7=15
  1. Subtract 7 from both sides of the equation.

    x=15−7x = 15 - 7
  2. Simplify the right side.

    x=8x = 8

    The solution is x=8\boxed{x=8}.

Part b· 2 steps

Solve for xx

−3x=−6-3x=-6
  1. Divide both sides of the equation by -3.

    x=−6−3x = \frac{-6}{-3}
  2. Simplify the fraction.

    x=2x = 2

    The solution is x=2\boxed{x=2}.

Part c· 3 steps

Solve for xx

9x−7=119x-7=11
  1. Add 7 to both sides of the equation.

    9x=11+79x = 11 + 7 9x=189x = 18
  2. Divide both sides by 9.

    x=189x = \frac{18}{9}
  3. Simplify the fraction.

    x=2x = 2

    The solution is x=2\boxed{x=2}.

Part d· 2 steps

Solve for xx

x4=−5\frac{x}{4}=-5
  1. Multiply both sides of the equation by 4.

    x=−5×4x = -5 \times 4
  2. Perform the multiplication.

    x=−20x = -20

    The solution is x=−20\boxed{x=-20}.

Part e· 3 steps

Solve for xx

−x3+1=3-\frac{x}{3}+1=3
  1. Subtract 1 from both sides of the equation.

    −x3=3−1-\frac{x}{3} = 3 - 1 −x3=2-\frac{x}{3} = 2
  2. Multiply both sides by -3.

    x=2×(−3)x = 2 \times (-3)
  3. Perform the multiplication.

    x=−6x = -6

    The solution is x=−6\boxed{x=-6}.

Part f· 3 steps

Solve for xx

3x−12=2\frac{3x-1}{2}=2
  1. Multiply both sides of the equation by 2.

    3x−1=2×23x-1 = 2 \times 2 3x−1=43x-1 = 4
  2. Add 1 to both sides.

    3x=4+13x = 4 + 1 3x=53x = 5
  3. Divide both sides by 3.

    x=53x = \frac{5}{3}

    The solution is x=53\boxed{x=\frac{5}{3}}.

Part g· 2 steps

Solve for xx

x−8=19x-8=19
  1. Add 8 to both sides of the equation.

    x=19+8x = 19 + 8
  2. Perform the addition.

    x=27x = 27

    The solution is x=27\boxed{x=27}.

Part h· 3 steps

Solve for xx

3x+5=293x+5=29
  1. Subtract 5 from both sides of the equation.

    3x=29−53x = 29 - 5 3x=243x = 24
  2. Divide both sides by 3.

    x=243x = \frac{24}{3}
  3. Simplify the fraction.

    x=8x = 8

    The solution is x=8\boxed{x=8}.

Part h(i)· 7 steps

Solve for mm

m3=6\frac{m}{3}=6
  1. Multiply both sides of the equation by 3.

    m=6×3m = 6 \times 3
  2. Perform the multiplication.

    m=18m = 18

    The solution is m=18\boxed{m=18}.

    j) Solve for xx:

    12(3x+1)+13(2x+10)=0\frac{1}{2}(3x+1)+\frac{1}{3}(2x+10)=0
  3. Multiply the entire equation by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions.

    6⋅12(3x+1)+6⋅13(2x+10)=6⋅06 \cdot \frac{1}{2}(3x+1) + 6 \cdot \frac{1}{3}(2x+10) = 6 \cdot 0 3(3x+1)+2(2x+10)=03(3x+1) + 2(2x+10) = 0
  4. Distribute the numbers into the parentheses.

    9x+3+4x+20=09x + 3 + 4x + 20 = 0
  5. Combine like terms (xx terms and constant terms).

    (9x+4x)+(3+20)=0(9x + 4x) + (3 + 20) = 0 13x+23=013x + 23 = 0
  6. Subtract 23 from both sides of the equation.

    13x=−2313x = -23
  7. Divide both sides by 13.

    x=−2313x = -\frac{23}{13}

    The solution is x=−2313\boxed{x=-\frac{23}{13}}.

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