Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(6x+2)=-10-(-5+x)\)
2. \(4(3x-1)=7+(-9+5x)\)
3. \(5(3x-3)=1+(2+2x)\)
4. \(4(4x+3)=-2+(13+3x)\)
5. \(2(x+6)=11+(6+3x)\)
6. \(3(2x-7)=7+(-8+x)\)
7. \(5(-5x-1)=-15+(-12-4x)\)
8. \(6(-5x-2)=8-(-1+x)\)
9. \(5(-x-5)=3-(-2+3x)\)
10. \(4(-2x-7)=9-(-7-5x)\)
11. \(5(4x-6)=8-(-5+x)\)
12. \(6(6x+7)=4-(-3+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+2)& = & -10 \color{red}{-} (-5+x) \\\Leftrightarrow & 18x+6& = &-10+5-x \\\Leftrightarrow & 18x \color{red}{+6} & = &-5 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &-5-6 \\\Leftrightarrow & 19x& = &-11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-1)& = & 7 \color{red}{+} (-9+5x) \\\Leftrightarrow & 12x-4& = &7-9+5x \\\Leftrightarrow & 12x \color{red}{-4} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 12x-5x& = &-2+4 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-3)& = & 1 \color{red}{+} (2+2x) \\\Leftrightarrow & 15x-15& = &1+2+2x \\\Leftrightarrow & 15x \color{red}{-15} & = &3 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 15x-2x& = &3+15 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x+3)& = & -2 \color{red}{+} (13+3x) \\\Leftrightarrow & 16x+12& = &-2+13+3x \\\Leftrightarrow & 16x \color{red}{+12} & = &11 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 16x-3x& = &11-12 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x+6)& = & 11 \color{red}{+} (6+3x) \\\Leftrightarrow & 2x+12& = &11+6+3x \\\Leftrightarrow & 2x \color{red}{+12} & = &17 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 2x-3x& = &17-12 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x-7)& = & 7 \color{red}{+} (-8+x) \\\Leftrightarrow & 6x-21& = &7-8+x \\\Leftrightarrow & 6x \color{red}{-21} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 6x-x& = &-1+21 \\\Leftrightarrow & 5x& = &20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{20}{ \color{red}{5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-1)& = & -15 \color{red}{+} (-12-4x) \\\Leftrightarrow & -25x-5& = &-15-12-4x \\\Leftrightarrow & -25x \color{red}{-5} & = &-27 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &-27 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & -25x+4x& = &-27+5 \\\Leftrightarrow & -21x& = &-22 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-22}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{22}{21} & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-2)& = & 8 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x-12& = &8+1-x \\\Leftrightarrow & -30x \color{red}{-12} & = &9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -30x+x& = &9+12 \\\Leftrightarrow & -29x& = &21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x-5)& = & 3 \color{red}{-} (-2+3x) \\\Leftrightarrow & -5x-25& = &3+2-3x \\\Leftrightarrow & -5x \color{red}{-25} & = &5 \color{red}{-3x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & -5x+3x& = &5+25 \\\Leftrightarrow & -2x& = &30 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{30}{ \color{red}{-2} } \\\Leftrightarrow & x = -15 & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-7)& = & 9 \color{red}{-} (-7-5x) \\\Leftrightarrow & -8x-28& = &9+7+5x \\\Leftrightarrow & -8x \color{red}{-28} & = &16 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & -8x-5x& = &16+28 \\\Leftrightarrow & -13x& = &44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-44}{13} & & \\ & V = \left\{ \frac{-44}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-6)& = & 8 \color{red}{-} (-5+x) \\\Leftrightarrow & 20x-30& = &8+5-x \\\Leftrightarrow & 20x \color{red}{-30} & = &13 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 20x+x& = &13+30 \\\Leftrightarrow & 21x& = &43 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{43}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{43}{21} & & \\ & V = \left\{ \frac{43}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x+7)& = & 4 \color{red}{-} (-3+x) \\\Leftrightarrow & 36x+42& = &4+3-x \\\Leftrightarrow & 36x \color{red}{+42} & = &7 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 36x+x& = &7-42 \\\Leftrightarrow & 37x& = &-35 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-35}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-35}{37} & & \\ & V = \left\{ \frac{-35}{37} \right\} & \\\end{align}\)