Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(3x-1)=1-(12+x)\)
2. \(6(4x+7)=-7-(10+x)\)
3. \(3(4x-7)=-1+(-11+x)\)
4. \(3(3x-1)=-14-(14+x)\)
5. \(6(6x-6)=-14+(-8+x)\)
6. \(2(2x+5)=-2+(-14+x)\)
7. \(4(3x-1)=-7+(-10+x)\)
8. \(3(-5x+1)=13+(3+x)\)
9. \(2(x+2)=-9-(-12+x)\)
10. \(5(4x-4)=-15+(9+x)\)
11. \(3(6x-6)=-14-(-5-5x)\)
12. \(5(-4x-4)=9+(-11+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x-1)& = & 1 \color{red}{-} (12+x) \\\Leftrightarrow & 18x-6& = &1-12-x \\\Leftrightarrow & 18x \color{red}{-6} & = &-11 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 18x+x& = &-11+6 \\\Leftrightarrow & 19x& = &-5 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-5}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+7)& = & -7 \color{red}{-} (10+x) \\\Leftrightarrow & 24x+42& = &-7-10-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-17-42 \\\Leftrightarrow & 25x& = &-59 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-59}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-59}{25} & & \\ & V = \left\{ \frac{-59}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-7)& = & -1 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x-21& = &-1-11+x \\\Leftrightarrow & 12x \color{red}{-21} & = &-12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &-12+21 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-1)& = & -14 \color{red}{-} (14+x) \\\Leftrightarrow & 9x-3& = &-14-14-x \\\Leftrightarrow & 9x \color{red}{-3} & = &-28 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 9x+x& = &-28+3 \\\Leftrightarrow & 10x& = &-25 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-25}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-6)& = & -14 \color{red}{+} (-8+x) \\\Leftrightarrow & 36x-36& = &-14-8+x \\\Leftrightarrow & 36x \color{red}{-36} & = &-22 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 36x-x& = &-22+36 \\\Leftrightarrow & 35x& = &14 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{14}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+5)& = & -2 \color{red}{+} (-14+x) \\\Leftrightarrow & 4x+10& = &-2-14+x \\\Leftrightarrow & 4x \color{red}{+10} & = &-16 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 4x-x& = &-16-10 \\\Leftrightarrow & 3x& = &-26 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-26}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-26}{3} & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-1)& = & -7 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x-4& = &-7-10+x \\\Leftrightarrow & 12x \color{red}{-4} & = &-17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &-17+4 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+1)& = & 13 \color{red}{+} (3+x) \\\Leftrightarrow & -15x+3& = &13+3+x \\\Leftrightarrow & -15x \color{red}{+3} & = &16 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -15x-x& = &16-3 \\\Leftrightarrow & -16x& = &13 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{13}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-13}{16} & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x+2)& = & -9 \color{red}{-} (-12+x) \\\Leftrightarrow & 2x+4& = &-9+12-x \\\Leftrightarrow & 2x \color{red}{+4} & = &3 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &3-4 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-4)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & 20x-20& = &-15+9+x \\\Leftrightarrow & 20x \color{red}{-20} & = &-6 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &-6+20 \\\Leftrightarrow & 19x& = &14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-6)& = & -14 \color{red}{-} (-5-5x) \\\Leftrightarrow & 18x-18& = &-14+5+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &-9+18 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-4)& = & 9 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x-20& = &9-11+x \\\Leftrightarrow & -20x \color{red}{-20} & = &-2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &-2+20 \\\Leftrightarrow & -21x& = &18 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{18}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)