Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(5(-x-6)=-14-(14+2x)\)
2. \(6(6x-3)=14+(14-5x)\)
3. \(4(-5x-1)=-6-(5+x)\)
4. \(3(-2x+1)=-5-(-3+x)\)
5. \(6(2x-3)=15+(7+x)\)
6. \(5(2x-2)=-12+(-10+x)\)
7. \(6(6x-5)=-4-(2+x)\)
8. \(6(-2x-4)=-11+(-12+x)\)
9. \(2(6x+7)=3-(-1+x)\)
10. \(4(-2x-7)=6-(2+x)\)
11. \(2(-2x-7)=15+(4-3x)\)
12. \(5(-3x-2)=-12+(-5+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x-6)& = & -14 \color{red}{-} (14+2x) \\\Leftrightarrow & -5x-30& = &-14-14-2x \\\Leftrightarrow & -5x \color{red}{-30} & = &-28 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -5x+2x& = &-28+30 \\\Leftrightarrow & -3x& = &2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-3)& = & 14 \color{red}{+} (14-5x) \\\Leftrightarrow & 36x-18& = &14+14-5x \\\Leftrightarrow & 36x \color{red}{-18} & = &28 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &28 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 36x+5x& = &28+18 \\\Leftrightarrow & 41x& = &46 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{46}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{46}{41} & & \\ & V = \left\{ \frac{46}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-1)& = & -6 \color{red}{-} (5+x) \\\Leftrightarrow & -20x-4& = &-6-5-x \\\Leftrightarrow & -20x \color{red}{-4} & = &-11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -20x+x& = &-11+4 \\\Leftrightarrow & -19x& = &-7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+1)& = & -5 \color{red}{-} (-3+x) \\\Leftrightarrow & -6x+3& = &-5+3-x \\\Leftrightarrow & -6x \color{red}{+3} & = &-2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -6x+x& = &-2-3 \\\Leftrightarrow & -5x& = &-5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-5}{ \color{red}{-5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-3)& = & 15 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-18& = &15+7+x \\\Leftrightarrow & 12x \color{red}{-18} & = &22 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &22+18 \\\Leftrightarrow & 11x& = &40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{40}{11} & & \\ & V = \left\{ \frac{40}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-2)& = & -12 \color{red}{+} (-10+x) \\\Leftrightarrow & 10x-10& = &-12-10+x \\\Leftrightarrow & 10x \color{red}{-10} & = &-22 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 10x-x& = &-22+10 \\\Leftrightarrow & 9x& = &-12 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-12}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x-5)& = & -4 \color{red}{-} (2+x) \\\Leftrightarrow & 36x-30& = &-4-2-x \\\Leftrightarrow & 36x \color{red}{-30} & = &-6 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 36x+x& = &-6+30 \\\Leftrightarrow & 37x& = &24 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{24}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{24}{37} & & \\ & V = \left\{ \frac{24}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x-4)& = & -11 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x-24& = &-11-12+x \\\Leftrightarrow & -12x \color{red}{-24} & = &-23 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &-23+24 \\\Leftrightarrow & -13x& = &1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x+7)& = & 3 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x+14& = &3+1-x \\\Leftrightarrow & 12x \color{red}{+14} & = &4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 12x+x& = &4-14 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-7)& = & 6 \color{red}{-} (2+x) \\\Leftrightarrow & -8x-28& = &6-2-x \\\Leftrightarrow & -8x \color{red}{-28} & = &4 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -8x+x& = &4+28 \\\Leftrightarrow & -7x& = &32 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{32}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-32}{7} & & \\ & V = \left\{ \frac{-32}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-7)& = & 15 \color{red}{+} (4-3x) \\\Leftrightarrow & -4x-14& = &15+4-3x \\\Leftrightarrow & -4x \color{red}{-14} & = &19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -4x+3x& = &19+14 \\\Leftrightarrow & -x& = &33 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{33}{ \color{red}{-1} } \\\Leftrightarrow & x = -33 & & \\ & V = \left\{ -33 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x-2)& = & -12 \color{red}{+} (-5+x) \\\Leftrightarrow & -15x-10& = &-12-5+x \\\Leftrightarrow & -15x \color{red}{-10} & = &-17 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -15x-x& = &-17+10 \\\Leftrightarrow & -16x& = &-7 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-7}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{7}{16} & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)