Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x+2)& = & -11 \color{red}{-} (-11+x) \\\Leftrightarrow & -12x+8& = &-11+11-x \\\Leftrightarrow & -12x \color{red}{+8} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &0-8 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x+1)& = & -2 \color{red}{+} (11+x) \\\Leftrightarrow & -30x+5& = &-2+11+x \\\Leftrightarrow & -30x \color{red}{+5} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -30x-x& = &9-5 \\\Leftrightarrow & -31x& = &4 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{4}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x-2)& = & 3 \color{red}{-} (12+x) \\\Leftrightarrow & 8x-4& = &3-12-x \\\Leftrightarrow & 8x \color{red}{-4} & = &-9 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &-9+4 \\\Leftrightarrow & 9x& = &-5 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-5}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-5}{9} & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x-5)& = & 12 \color{red}{+} (-5+x) \\\Leftrightarrow & 12x-20& = &12-5+x \\\Leftrightarrow & 12x \color{red}{-20} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 12x-x& = &7+20 \\\Leftrightarrow & 11x& = &27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{27}{11} & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x-2)& = & -14 \color{red}{-} (2+4x) \\\Leftrightarrow & 5x-10& = &-14-2-4x \\\Leftrightarrow & 5x \color{red}{-10} & = &-16 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &-16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & 5x+4x& = &-16+10 \\\Leftrightarrow & 9x& = &-6 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-6}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-7)& = & 6 \color{red}{-} (-1+x) \\\Leftrightarrow & 16x-28& = &6+1-x \\\Leftrightarrow & 16x \color{red}{-28} & = &7 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 16x+x& = &7+28 \\\Leftrightarrow & 17x& = &35 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{35}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{35}{17} & & \\ & V = \left\{ \frac{35}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-2)& = & 13 \color{red}{-} (-4+x) \\\Leftrightarrow & -20x-10& = &13+4-x \\\Leftrightarrow & -20x \color{red}{-10} & = &17 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &17+10 \\\Leftrightarrow & -19x& = &27 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{27}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-5)& = & -12 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x-30& = &-12+11-x \\\Leftrightarrow & 24x \color{red}{-30} & = &-1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &-1+30 \\\Leftrightarrow & 25x& = &29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x+5)& = & 9 \color{red}{+} (11+x) \\\Leftrightarrow & -16x+20& = &9+11+x \\\Leftrightarrow & -16x \color{red}{+20} & = &20 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -16x-x& = &20-20 \\\Leftrightarrow & -17x& = &0 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{0}{ \color{red}{-17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-5)& = & 10 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x-10& = &10-9+x \\\Leftrightarrow & 2x \color{red}{-10} & = &1 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 2x-x& = &1+10 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-5)& = & -6 \color{red}{+} (2+3x) \\\Leftrightarrow & 20x-25& = &-6+2+3x \\\Leftrightarrow & 20x \color{red}{-25} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & 20x-3x& = &-4+25 \\\Leftrightarrow & 17x& = &21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+2)& = & 15 \color{red}{-} (15+x) \\\Leftrightarrow & 18x+12& = &15-15-x \\\Leftrightarrow & 18x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &0-12 \\\Leftrightarrow & 19x& = &-12 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-12}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)