Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-2)& = & 3 \color{red}{-} (4+x) \\\Leftrightarrow & -18x-12& = &3-4-x \\\Leftrightarrow & -18x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &-1+12 \\\Leftrightarrow & -17x& = &11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+6)& = & 3 \color{red}{+} (-14-2x) \\\Leftrightarrow & 3x+18& = &3-14-2x \\\Leftrightarrow & 3x \color{red}{+18} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & 3x+2x& = &-11-18 \\\Leftrightarrow & 5x& = &-29 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-29}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-29}{5} & & \\ & V = \left\{ \frac{-29}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+7)& = & -4 \color{red}{-} (1-3x) \\\Leftrightarrow & 10x+14& = &-4-1+3x \\\Leftrightarrow & 10x \color{red}{+14} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 10x-3x& = &-5-14 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+1)& = & 13 \color{red}{-} (-10-2x) \\\Leftrightarrow & -15x+3& = &13+10+2x \\\Leftrightarrow & -15x \color{red}{+3} & = &23 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -15x-2x& = &23-3 \\\Leftrightarrow & -17x& = &20 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{20}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-20}{17} & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-x+3)& = & 12 \color{red}{+} (3+3x) \\\Leftrightarrow & -2x+6& = &12+3+3x \\\Leftrightarrow & -2x \color{red}{+6} & = &15 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -2x-3x& = &15-6 \\\Leftrightarrow & -5x& = &9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+5)& = & -11 \color{red}{+} (9+x) \\\Leftrightarrow & 12x+20& = &-11+9+x \\\Leftrightarrow & 12x \color{red}{+20} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 12x-x& = &-2-20 \\\Leftrightarrow & 11x& = &-22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-22}{ \color{red}{11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x+5)& = & -10 \color{red}{-} (-8+x) \\\Leftrightarrow & 8x+20& = &-10+8-x \\\Leftrightarrow & 8x \color{red}{+20} & = &-2 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 8x+x& = &-2-20 \\\Leftrightarrow & 9x& = &-22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x+2)& = & 3 \color{red}{+} (14+x) \\\Leftrightarrow & -30x+12& = &3+14+x \\\Leftrightarrow & -30x \color{red}{+12} & = &17 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -30x-x& = &17-12 \\\Leftrightarrow & -31x& = &5 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{5}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-5}{31} & & \\ & V = \left\{ \frac{-5}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x-1)& = & 4 \color{red}{+} (-7+x) \\\Leftrightarrow & 30x-6& = &4-7+x \\\Leftrightarrow & 30x \color{red}{-6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &-3+6 \\\Leftrightarrow & 29x& = &3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{3}{29} & & \\ & V = \left\{ \frac{3}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-3)& = & 10 \color{red}{-} (-6+x) \\\Leftrightarrow & -9x-9& = &10+6-x \\\Leftrightarrow & -9x \color{red}{-9} & = &16 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -9x+x& = &16+9 \\\Leftrightarrow & -8x& = &25 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{25}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-25}{8} & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+3)& = & 10 \color{red}{-} (-1+x) \\\Leftrightarrow & -20x+12& = &10+1-x \\\Leftrightarrow & -20x \color{red}{+12} & = &11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -20x+x& = &11-12 \\\Leftrightarrow & -19x& = &-1 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-1}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x-5)& = & -14 \color{red}{-} (-13+3x) \\\Leftrightarrow & 4x-20& = &-14+13-3x \\\Leftrightarrow & 4x \color{red}{-20} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 4x+3x& = &-1+20 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)