Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+6)& = & -6 \color{red}{-} (-3+x) \\\Leftrightarrow & 18x+18& = &-6+3-x \\\Leftrightarrow & 18x \color{red}{+18} & = &-3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 18x+x& = &-3-18 \\\Leftrightarrow & 19x& = &-21 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-21}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-21}{19} & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+2)& = & 8 \color{red}{-} (12+x) \\\Leftrightarrow & 2x+4& = &8-12-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-4-4 \\\Leftrightarrow & 3x& = &-8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x+3)& = & -15 \color{red}{-} (5+x) \\\Leftrightarrow & -18x+18& = &-15-5-x \\\Leftrightarrow & -18x \color{red}{+18} & = &-20 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -18x+x& = &-20-18 \\\Leftrightarrow & -17x& = &-38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{38}{17} & & \\ & V = \left\{ \frac{38}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+3)& = & -15 \color{red}{-} (2+x) \\\Leftrightarrow & 36x+18& = &-15-2-x \\\Leftrightarrow & 36x \color{red}{+18} & = &-17 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 36x+x& = &-17-18 \\\Leftrightarrow & 37x& = &-35 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-35}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-35}{37} & & \\ & V = \left\{ \frac{-35}{37} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+5)& = & 9 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x+20& = &9+12-x \\\Leftrightarrow & -24x \color{red}{+20} & = &21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &21-20 \\\Leftrightarrow & -23x& = &1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+7)& = & 12 \color{red}{-} (-15+x) \\\Leftrightarrow & -30x+35& = &12+15-x \\\Leftrightarrow & -30x \color{red}{+35} & = &27 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -30x+x& = &27-35 \\\Leftrightarrow & -29x& = &-8 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-8}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{8}{29} & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x+4)& = & 1 \color{red}{-} (-7+x) \\\Leftrightarrow & 15x+12& = &1+7-x \\\Leftrightarrow & 15x \color{red}{+12} & = &8 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 15x+x& = &8-12 \\\Leftrightarrow & 16x& = &-4 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-4}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+6)& = & -1 \color{red}{-} (-14-5x) \\\Leftrightarrow & 6x+12& = &-1+14+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &13 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &13-12 \\\Leftrightarrow & x& = &1 \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-2)& = & 10 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x-10& = &10-6+x \\\Leftrightarrow & -30x \color{red}{-10} & = &4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -30x-x& = &4+10 \\\Leftrightarrow & -31x& = &14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-5)& = & 2 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x-20& = &2+15-x \\\Leftrightarrow & 20x \color{red}{-20} & = &17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 20x+x& = &17+20 \\\Leftrightarrow & 21x& = &37 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{37}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{37}{21} & & \\ & V = \left\{ \frac{37}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x-3)& = & -6 \color{red}{+} (-8-5x) \\\Leftrightarrow & -16x-12& = &-6-8-5x \\\Leftrightarrow & -16x \color{red}{-12} & = &-14 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -16x+5x& = &-14+12 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-1)& = & 4 \color{red}{-} (-15-4x) \\\Leftrightarrow & -5x-5& = &4+15+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &19 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &19 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &19+5 \\\Leftrightarrow & -9x& = &24 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{24}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)