Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x-5)& = & 7 \color{red}{+} (-8-5x) \\\Leftrightarrow & -6x-10& = &7-8-5x \\\Leftrightarrow & -6x \color{red}{-10} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & -6x+5x& = &-1+10 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-1)& = & 12 \color{red}{+} (-15-5x) \\\Leftrightarrow & -18x-6& = &12-15-5x \\\Leftrightarrow & -18x \color{red}{-6} & = &-3 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -18x+5x& = &-3+6 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+7)& = & -15 \color{red}{+} (-5+x) \\\Leftrightarrow & 24x+42& = &-15-5+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-20 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-20-42 \\\Leftrightarrow & 23x& = &-62 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-62}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-62}{23} & & \\ & V = \left\{ \frac{-62}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x-5)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -20x-25& = &3-14-x \\\Leftrightarrow & -20x \color{red}{-25} & = &-11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -20x+x& = &-11+25 \\\Leftrightarrow & -19x& = &14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+7)& = & -2 \color{red}{+} (15+x) \\\Leftrightarrow & -36x+42& = &-2+15+x \\\Leftrightarrow & -36x \color{red}{+42} & = &13 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -36x-x& = &13-42 \\\Leftrightarrow & -37x& = &-29 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-29}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{29}{37} & & \\ & V = \left\{ \frac{29}{37} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x-4)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 2x-8& = &2-2-x \\\Leftrightarrow & 2x \color{red}{-8} & = &0 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 2x+x& = &0+8 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x+1)& = & 3 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x+4& = &3+3-x \\\Leftrightarrow & -12x \color{red}{+4} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &6-4 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x+4)& = & 12 \color{red}{+} (-7-4x) \\\Leftrightarrow & -25x+20& = &12-7-4x \\\Leftrightarrow & -25x \color{red}{+20} & = &5 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & -25x+4x& = &5-20 \\\Leftrightarrow & -21x& = &-15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-7)& = & 4 \color{red}{+} (14+x) \\\Leftrightarrow & -2x-14& = &4+14+x \\\Leftrightarrow & -2x \color{red}{-14} & = &18 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -2x-x& = &18+14 \\\Leftrightarrow & -3x& = &32 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{32}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-32}{3} & & \\ & V = \left\{ \frac{-32}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-6)& = & 7 \color{red}{-} (-5+x) \\\Leftrightarrow & 24x-36& = &7+5-x \\\Leftrightarrow & 24x \color{red}{-36} & = &12 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &12+36 \\\Leftrightarrow & 25x& = &48 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{48}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{48}{25} & & \\ & V = \left\{ \frac{48}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-6)& = & 9 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-24& = &9+12-x \\\Leftrightarrow & -24x \color{red}{-24} & = &21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &21+24 \\\Leftrightarrow & -23x& = &45 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{45}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-45}{23} & & \\ & V = \left\{ \frac{-45}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+4)& = & 5 \color{red}{+} (-5+2x) \\\Leftrightarrow & -15x+20& = &5-5+2x \\\Leftrightarrow & -15x \color{red}{+20} & = &0 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -15x-2x& = &0-20 \\\Leftrightarrow & -17x& = &-20 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-20}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{20}{17} & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)