Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+2)& = & -12 \color{red}{+} (-5+x) \\\Leftrightarrow & -15x+10& = &-12-5+x \\\Leftrightarrow & -15x \color{red}{+10} & = &-17 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -15x-x& = &-17-10 \\\Leftrightarrow & -16x& = &-27 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-27}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{27}{16} & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+7)& = & 11 \color{red}{+} (-11+4x) \\\Leftrightarrow & 25x+35& = &11-11+4x \\\Leftrightarrow & 25x \color{red}{+35} & = &0 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-35} \\\Leftrightarrow & 25x-4x& = &0-35 \\\Leftrightarrow & 21x& = &-35 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-35}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-4)& = & 9 \color{red}{-} (4+x) \\\Leftrightarrow & -30x-20& = &9-4-x \\\Leftrightarrow & -30x \color{red}{-20} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &5+20 \\\Leftrightarrow & -29x& = &25 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{25}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-25}{29} & & \\ & V = \left\{ \frac{-25}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-3)& = & 8 \color{red}{+} (13+x) \\\Leftrightarrow & -4x-6& = &8+13+x \\\Leftrightarrow & -4x \color{red}{-6} & = &21 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -4x-x& = &21+6 \\\Leftrightarrow & -5x& = &27 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{27}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-27}{5} & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x+6)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x+12& = &13+1-x \\\Leftrightarrow & -12x \color{red}{+12} & = &14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &14-12 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+6)& = & 1 \color{red}{+} (14+x) \\\Leftrightarrow & 24x+36& = &1+14+x \\\Leftrightarrow & 24x \color{red}{+36} & = &15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 24x-x& = &15-36 \\\Leftrightarrow & 23x& = &-21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x-6)& = & -13 \color{red}{+} (1-3x) \\\Leftrightarrow & 4x-12& = &-13+1-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &-12+12 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+5)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & -24x+20& = &4+5+x \\\Leftrightarrow & -24x \color{red}{+20} & = &9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -24x-x& = &9-20 \\\Leftrightarrow & -25x& = &-11 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-11}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{11}{25} & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+2)& = & 5 \color{red}{+} (-7-5x) \\\Leftrightarrow & 3x+6& = &5-7-5x \\\Leftrightarrow & 3x \color{red}{+6} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 3x+5x& = &-2-6 \\\Leftrightarrow & 8x& = &-8 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-8}{ \color{red}{8} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-1)& = & 4 \color{red}{+} (-4+x) \\\Leftrightarrow & 24x-4& = &4-4+x \\\Leftrightarrow & 24x \color{red}{-4} & = &0 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 24x-x& = &0+4 \\\Leftrightarrow & 23x& = &4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+7)& = & 6 \color{red}{-} (-10+x) \\\Leftrightarrow & -8x+14& = &6+10-x \\\Leftrightarrow & -8x \color{red}{+14} & = &16 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -8x+x& = &16-14 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+5)& = & 12 \color{red}{-} (12+x) \\\Leftrightarrow & -2x+10& = &12-12-x \\\Leftrightarrow & -2x \color{red}{+10} & = &0 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -2x+x& = &0-10 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)