Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-5)& = & 8 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-10& = &8-7+x \\\Leftrightarrow & -12x \color{red}{-10} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -12x-x& = &1+10 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-3)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & 9x-9& = &-4+8-x \\\Leftrightarrow & 9x \color{red}{-9} & = &4 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 9x+x& = &4+9 \\\Leftrightarrow & 10x& = &13 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{13}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{13}{10} & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-4)& = & -11 \color{red}{-} (-13-4x) \\\Leftrightarrow & -25x-20& = &-11+13+4x \\\Leftrightarrow & -25x \color{red}{-20} & = &2 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -25x-4x& = &2+20 \\\Leftrightarrow & -29x& = &22 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{22}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-22}{29} & & \\ & V = \left\{ \frac{-22}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-4)& = & 9 \color{red}{-} (-11+x) \\\Leftrightarrow & -8x-8& = &9+11-x \\\Leftrightarrow & -8x \color{red}{-8} & = &20 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &20+8 \\\Leftrightarrow & -7x& = &28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{28}{ \color{red}{-7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-1)& = & -9 \color{red}{-} (-4+4x) \\\Leftrightarrow & 15x-5& = &-9+4-4x \\\Leftrightarrow & 15x \color{red}{-5} & = &-5 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &-5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & 15x+4x& = &-5+5 \\\Leftrightarrow & 19x& = &0 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{0}{ \color{red}{19} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-5)& = & 11 \color{red}{-} (1-2x) \\\Leftrightarrow & -15x-25& = &11-1+2x \\\Leftrightarrow & -15x \color{red}{-25} & = &10 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -15x-2x& = &10+25 \\\Leftrightarrow & -17x& = &35 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{35}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-35}{17} & & \\ & V = \left\{ \frac{-35}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+3)& = & 11 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x+18& = &11-2+x \\\Leftrightarrow & -12x \color{red}{+18} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &9-18 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+6)& = & -9 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+24& = &-9+5-x \\\Leftrightarrow & -12x \color{red}{+24} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &-4-24 \\\Leftrightarrow & -11x& = &-28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+5)& = & -1 \color{red}{+} (-15-2x) \\\Leftrightarrow & -5x+25& = &-1-15-2x \\\Leftrightarrow & -5x \color{red}{+25} & = &-16 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &-16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & -5x+2x& = &-16-25 \\\Leftrightarrow & -3x& = &-41 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-41}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{41}{3} & & \\ & V = \left\{ \frac{41}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-7)& = & -13 \color{red}{+} (-3+3x) \\\Leftrightarrow & 20x-35& = &-13-3+3x \\\Leftrightarrow & 20x \color{red}{-35} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 20x-3x& = &-16+35 \\\Leftrightarrow & 17x& = &19 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{19}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{19}{17} & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x-2)& = & 14 \color{red}{-} (12+x) \\\Leftrightarrow & 24x-8& = &14-12-x \\\Leftrightarrow & 24x \color{red}{-8} & = &2 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 24x+x& = &2+8 \\\Leftrightarrow & 25x& = &10 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{10}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-5)& = & -1 \color{red}{+} (6+x) \\\Leftrightarrow & -30x-30& = &-1+6+x \\\Leftrightarrow & -30x \color{red}{-30} & = &5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &5+30 \\\Leftrightarrow & -31x& = &35 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{35}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-35}{31} & & \\ & V = \left\{ \frac{-35}{31} \right\} & \\\end{align}\)