Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+3)& = & -15 \color{red}{+} (14-5x) \\\Leftrightarrow & -18x+9& = &-15+14-5x \\\Leftrightarrow & -18x \color{red}{+9} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -18x+5x& = &-1-9 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-7)& = & -9 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x-21& = &-9-2+x \\\Leftrightarrow & 12x \color{red}{-21} & = &-11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &-11+21 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+3)& = & 13 \color{red}{+} (14+x) \\\Leftrightarrow & -24x+18& = &13+14+x \\\Leftrightarrow & -24x \color{red}{+18} & = &27 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -24x-x& = &27-18 \\\Leftrightarrow & -25x& = &9 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{9}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-9}{25} & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x+6)& = & -9 \color{red}{+} (-5-3x) \\\Leftrightarrow & -16x+24& = &-9-5-3x \\\Leftrightarrow & -16x \color{red}{+24} & = &-14 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -16x+3x& = &-14-24 \\\Leftrightarrow & -13x& = &-38 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-38}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{38}{13} & & \\ & V = \left\{ \frac{38}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-4)& = & 7 \color{red}{+} (-6+x) \\\Leftrightarrow & 15x-20& = &7-6+x \\\Leftrightarrow & 15x \color{red}{-20} & = &1 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 15x-x& = &1+20 \\\Leftrightarrow & 14x& = &21 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{21}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{3}{2} & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+4)& = & -11 \color{red}{+} (15+x) \\\Leftrightarrow & -24x+16& = &-11+15+x \\\Leftrightarrow & -24x \color{red}{+16} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -24x-x& = &4-16 \\\Leftrightarrow & -25x& = &-12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{12}{25} & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+4)& = & 4 \color{red}{-} (-10-3x) \\\Leftrightarrow & -4x+8& = &4+10+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &14 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &14-8 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x-7)& = & 5 \color{red}{+} (-9+x) \\\Leftrightarrow & 10x-35& = &5-9+x \\\Leftrightarrow & 10x \color{red}{-35} & = &-4 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 10x-x& = &-4+35 \\\Leftrightarrow & 9x& = &31 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{31}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{31}{9} & & \\ & V = \left\{ \frac{31}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+5)& = & 9 \color{red}{-} (-5+x) \\\Leftrightarrow & -5x+25& = &9+5-x \\\Leftrightarrow & -5x \color{red}{+25} & = &14 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -5x+x& = &14-25 \\\Leftrightarrow & -4x& = &-11 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-11}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{11}{4} & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+7)& = & -3 \color{red}{-} (-10+3x) \\\Leftrightarrow & 20x+28& = &-3+10-3x \\\Leftrightarrow & 20x \color{red}{+28} & = &7 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & 20x+3x& = &7-28 \\\Leftrightarrow & 23x& = &-21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x+3)& = & -10 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x+9& = &-10+3-x \\\Leftrightarrow & -12x \color{red}{+9} & = &-7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &-7-9 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+1)& = & 3 \color{red}{-} (-3+x) \\\Leftrightarrow & 18x+3& = &3+3-x \\\Leftrightarrow & 18x \color{red}{+3} & = &6 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 18x+x& = &6-3 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)