Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x-2)& = & 11 \color{red}{+} (-4+x) \\\Leftrightarrow & 6x-6& = &11-4+x \\\Leftrightarrow & 6x \color{red}{-6} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 6x-x& = &7+6 \\\Leftrightarrow & 5x& = &13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-4)& = & 10 \color{red}{+} (1+x) \\\Leftrightarrow & 36x-24& = &10+1+x \\\Leftrightarrow & 36x \color{red}{-24} & = &11 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 36x-x& = &11+24 \\\Leftrightarrow & 35x& = &35 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{35}{ \color{red}{35} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+5)& = & -2 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x+30& = &-2-14+x \\\Leftrightarrow & -24x \color{red}{+30} & = &-16 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &-16-30 \\\Leftrightarrow & -25x& = &-46 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-46}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{46}{25} & & \\ & V = \left\{ \frac{46}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-7)& = & -3 \color{red}{-} (14+x) \\\Leftrightarrow & 20x-35& = &-3-14-x \\\Leftrightarrow & 20x \color{red}{-35} & = &-17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 20x+x& = &-17+35 \\\Leftrightarrow & 21x& = &18 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{18}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x+3)& = & 3 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+18& = &3-4-x \\\Leftrightarrow & 12x \color{red}{+18} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &-1-18 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x+6)& = & 1 \color{red}{-} (-15+x) \\\Leftrightarrow & 18x+18& = &1+15-x \\\Leftrightarrow & 18x \color{red}{+18} & = &16 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 18x+x& = &16-18 \\\Leftrightarrow & 19x& = &-2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-4)& = & 13 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x-24& = &13-13+x \\\Leftrightarrow & 6x \color{red}{-24} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 6x-x& = &0+24 \\\Leftrightarrow & 5x& = &24 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{24}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{24}{5} & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-2)& = & -9 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x-12& = &-9-1+x \\\Leftrightarrow & 30x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 30x-x& = &-10+12 \\\Leftrightarrow & 29x& = &2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+6)& = & -9 \color{red}{-} (2+4x) \\\Leftrightarrow & 15x+30& = &-9-2-4x \\\Leftrightarrow & 15x \color{red}{+30} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 15x+4x& = &-11-30 \\\Leftrightarrow & 19x& = &-41 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-41}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-41}{19} & & \\ & V = \left\{ \frac{-41}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+4)& = & -1 \color{red}{+} (-4-5x) \\\Leftrightarrow & 16x+16& = &-1-4-5x \\\Leftrightarrow & 16x \color{red}{+16} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-16} \\\Leftrightarrow & 16x+5x& = &-5-16 \\\Leftrightarrow & 21x& = &-21 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-21}{ \color{red}{21} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-6)& = & 9 \color{red}{-} (3+3x) \\\Leftrightarrow & 5x-30& = &9-3-3x \\\Leftrightarrow & 5x \color{red}{-30} & = &6 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & 5x+3x& = &6+30 \\\Leftrightarrow & 8x& = &36 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{36}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{9}{2} & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x-2)& = & 3 \color{red}{-} (-3-5x) \\\Leftrightarrow & 36x-12& = &3+3+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &6 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &6+12 \\\Leftrightarrow & 31x& = &18 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{18}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{18}{31} & & \\ & V = \left\{ \frac{18}{31} \right\} & \\\end{align}\)