Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x-5)& = & 9 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x-25& = &9-1+x \\\Leftrightarrow & 30x \color{red}{-25} & = &8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 30x-x& = &8+25 \\\Leftrightarrow & 29x& = &33 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{33}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{33}{29} & & \\ & V = \left\{ \frac{33}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x-7)& = & -9 \color{red}{+} (4+x) \\\Leftrightarrow & 20x-35& = &-9+4+x \\\Leftrightarrow & 20x \color{red}{-35} & = &-5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 20x-x& = &-5+35 \\\Leftrightarrow & 19x& = &30 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{30}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{30}{19} & & \\ & V = \left\{ \frac{30}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x-7)& = & -7 \color{red}{+} (-13-2x) \\\Leftrightarrow & -5x-35& = &-7-13-2x \\\Leftrightarrow & -5x \color{red}{-35} & = &-20 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -5x+2x& = &-20+35 \\\Leftrightarrow & -3x& = &15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{15}{ \color{red}{-3} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-2)& = & 6 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-12& = &6-8+x \\\Leftrightarrow & -30x \color{red}{-12} & = &-2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &-2+12 \\\Leftrightarrow & -31x& = &10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-4)& = & -1 \color{red}{+} (-15+x) \\\Leftrightarrow & 12x-16& = &-1-15+x \\\Leftrightarrow & 12x \color{red}{-16} & = &-16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &-16+16 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-5)& = & -1 \color{red}{+} (15+x) \\\Leftrightarrow & 6x-10& = &-1+15+x \\\Leftrightarrow & 6x \color{red}{-10} & = &14 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 6x-x& = &14+10 \\\Leftrightarrow & 5x& = &24 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{24}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{24}{5} & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+2)& = & 6 \color{red}{+} (3+x) \\\Leftrightarrow & 36x+12& = &6+3+x \\\Leftrightarrow & 36x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 36x-x& = &9-12 \\\Leftrightarrow & 35x& = &-3 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-3}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-7)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-14& = &-11-11-x \\\Leftrightarrow & 12x \color{red}{-14} & = &-22 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &-22+14 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+4)& = & 6 \color{red}{+} (-8+x) \\\Leftrightarrow & 9x+12& = &6-8+x \\\Leftrightarrow & 9x \color{red}{+12} & = &-2 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 9x-x& = &-2-12 \\\Leftrightarrow & 8x& = &-14 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-14}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-7}{4} & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-4)& = & 1 \color{red}{-} (-5+3x) \\\Leftrightarrow & -10x-8& = &1+5-3x \\\Leftrightarrow & -10x \color{red}{-8} & = &6 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -10x+3x& = &6+8 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x-6)& = & 4 \color{red}{-} (-14+x) \\\Leftrightarrow & 25x-30& = &4+14-x \\\Leftrightarrow & 25x \color{red}{-30} & = &18 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 25x+x& = &18+30 \\\Leftrightarrow & 26x& = &48 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{48}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-1)& = & 14 \color{red}{-} (-11-2x) \\\Leftrightarrow & -9x-3& = &14+11+2x \\\Leftrightarrow & -9x \color{red}{-3} & = &25 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &25 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & -9x-2x& = &25+3 \\\Leftrightarrow & -11x& = &28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)