Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-4)& = & -3 \color{red}{+} (-7+x) \\\Leftrightarrow & -36x-24& = &-3-7+x \\\Leftrightarrow & -36x \color{red}{-24} & = &-10 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &-10+24 \\\Leftrightarrow & -37x& = &14 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{14}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-14}{37} & & \\ & V = \left\{ \frac{-14}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+7)& = & 9 \color{red}{-} (-2+3x) \\\Leftrightarrow & 2x+14& = &9+2-3x \\\Leftrightarrow & 2x \color{red}{+14} & = &11 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 2x+3x& = &11-14 \\\Leftrightarrow & 5x& = &-3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-1)& = & 13 \color{red}{+} (-12+x) \\\Leftrightarrow & -25x-5& = &13-12+x \\\Leftrightarrow & -25x \color{red}{-5} & = &1 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -25x-x& = &1+5 \\\Leftrightarrow & -26x& = &6 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{6}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-3)& = & -7 \color{red}{+} (-4+x) \\\Leftrightarrow & 16x-12& = &-7-4+x \\\Leftrightarrow & 16x \color{red}{-12} & = &-11 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 16x-x& = &-11+12 \\\Leftrightarrow & 15x& = &1 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{1}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x-1)& = & 14 \color{red}{+} (8-5x) \\\Leftrightarrow & 6x-2& = &14+8-5x \\\Leftrightarrow & 6x \color{red}{-2} & = &22 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{+5x} & = &22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+2} \\\Leftrightarrow & 6x+5x& = &22+2 \\\Leftrightarrow & 11x& = &24 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{24}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-2)& = & -13 \color{red}{-} (-12+x) \\\Leftrightarrow & -20x-10& = &-13+12-x \\\Leftrightarrow & -20x \color{red}{-10} & = &-1 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &-1+10 \\\Leftrightarrow & -19x& = &9 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{9}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-9}{19} & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x-7)& = & -2 \color{red}{+} (-4+x) \\\Leftrightarrow & -16x-28& = &-2-4+x \\\Leftrightarrow & -16x \color{red}{-28} & = &-6 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -16x-x& = &-6+28 \\\Leftrightarrow & -17x& = &22 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{22}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-22}{17} & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-2)& = & -13 \color{red}{+} (-8+x) \\\Leftrightarrow & 30x-12& = &-13-8+x \\\Leftrightarrow & 30x \color{red}{-12} & = &-21 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 30x-x& = &-21+12 \\\Leftrightarrow & 29x& = &-9 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-9}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-9}{29} & & \\ & V = \left\{ \frac{-9}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x-7)& = & 6 \color{red}{-} (-10-3x) \\\Leftrightarrow & 10x-35& = &6+10+3x \\\Leftrightarrow & 10x \color{red}{-35} & = &16 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 10x-3x& = &16+35 \\\Leftrightarrow & 7x& = &51 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{51}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{51}{7} & & \\ & V = \left\{ \frac{51}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-5x-6)& = & 5 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x-36& = &5+1-x \\\Leftrightarrow & -30x \color{red}{-36} & = &6 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -30x+x& = &6+36 \\\Leftrightarrow & -29x& = &42 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{42}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-42}{29} & & \\ & V = \left\{ \frac{-42}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x+3)& = & 15 \color{red}{+} (8-2x) \\\Leftrightarrow & 5x+15& = &15+8-2x \\\Leftrightarrow & 5x \color{red}{+15} & = &23 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &23 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 5x+2x& = &23-15 \\\Leftrightarrow & 7x& = &8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x+3)& = & -1 \color{red}{-} (2+x) \\\Leftrightarrow & -12x+18& = &-1-2-x \\\Leftrightarrow & -12x \color{red}{+18} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &-3-18 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)