Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x-6)& = & 4 \color{red}{+} (5-5x) \\\Leftrightarrow & -6x-36& = &4+5-5x \\\Leftrightarrow & -6x \color{red}{-36} & = &9 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -6x+5x& = &9+36 \\\Leftrightarrow & -x& = &45 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{45}{ \color{red}{-1} } \\\Leftrightarrow & x = -45 & & \\ & V = \left\{ -45 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+3)& = & -10 \color{red}{+} (3-4x) \\\Leftrightarrow & -5x+15& = &-10+3-4x \\\Leftrightarrow & -5x \color{red}{+15} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -5x+4x& = &-7-15 \\\Leftrightarrow & -x& = &-22 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-22}{ \color{red}{-1} } \\\Leftrightarrow & x = 22 & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-1)& = & 10 \color{red}{-} (8+x) \\\Leftrightarrow & 36x-6& = &10-8-x \\\Leftrightarrow & 36x \color{red}{-6} & = &2 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 36x+x& = &2+6 \\\Leftrightarrow & 37x& = &8 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{8}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{8}{37} & & \\ & V = \left\{ \frac{8}{37} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (x-2)& = & 5 \color{red}{+} (2-2x) \\\Leftrightarrow & 5x-10& = &5+2-2x \\\Leftrightarrow & 5x \color{red}{-10} & = &7 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & 5x+2x& = &7+10 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+7)& = & -10 \color{red}{+} (1+x) \\\Leftrightarrow & -10x+35& = &-10+1+x \\\Leftrightarrow & -10x \color{red}{+35} & = &-9 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -10x-x& = &-9-35 \\\Leftrightarrow & -11x& = &-44 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-44}{ \color{red}{-11} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x-6)& = & -2 \color{red}{+} (-2+x) \\\Leftrightarrow & 20x-24& = &-2-2+x \\\Leftrightarrow & 20x \color{red}{-24} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &-4+24 \\\Leftrightarrow & 19x& = &20 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{20}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{20}{19} & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x-3)& = & -8 \color{red}{-} (11+4x) \\\Leftrightarrow & 15x-9& = &-8-11-4x \\\Leftrightarrow & 15x \color{red}{-9} & = &-19 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &-19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & 15x+4x& = &-19+9 \\\Leftrightarrow & 19x& = &-10 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-10}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-10}{19} & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x+2)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & -2x+4& = &-2+14-x \\\Leftrightarrow & -2x \color{red}{+4} & = &12 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -2x+x& = &12-4 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-5)& = & -1 \color{red}{-} (1+x) \\\Leftrightarrow & 12x-30& = &-1-1-x \\\Leftrightarrow & 12x \color{red}{-30} & = &-2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 12x+x& = &-2+30 \\\Leftrightarrow & 13x& = &28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+2)& = & -3 \color{red}{+} (13+2x) \\\Leftrightarrow & -15x+6& = &-3+13+2x \\\Leftrightarrow & -15x \color{red}{+6} & = &10 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -15x-2x& = &10-6 \\\Leftrightarrow & -17x& = &4 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{4}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-7)& = & 1 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-14& = &1+12-x \\\Leftrightarrow & 12x \color{red}{-14} & = &13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &13+14 \\\Leftrightarrow & 13x& = &27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-3)& = & -2 \color{red}{+} (14+x) \\\Leftrightarrow & 2x-6& = &-2+14+x \\\Leftrightarrow & 2x \color{red}{-6} & = &12 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 2x-x& = &12+6 \\\Leftrightarrow & x& = &18 \\ & V = \left\{ 18 \right\} & \\\end{align}\)