Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+3)& = & 2 \color{red}{-} (-6+x) \\\Leftrightarrow & -8x+6& = &2+6-x \\\Leftrightarrow & -8x \color{red}{+6} & = &8 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -8x+x& = &8-6 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-5)& = & -7 \color{red}{+} (5-4x) \\\Leftrightarrow & 5x-25& = &-7+5-4x \\\Leftrightarrow & 5x \color{red}{-25} & = &-2 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 5x+4x& = &-2+25 \\\Leftrightarrow & 9x& = &23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+1)& = & -8 \color{red}{+} (-8+x) \\\Leftrightarrow & 18x+3& = &-8-8+x \\\Leftrightarrow & 18x \color{red}{+3} & = &-16 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 18x-x& = &-16-3 \\\Leftrightarrow & 17x& = &-19 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-19}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-19}{17} & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+3)& = & 14 \color{red}{+} (-2-3x) \\\Leftrightarrow & 4x+6& = &14-2-3x \\\Leftrightarrow & 4x \color{red}{+6} & = &12 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 4x+3x& = &12-6 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-3)& = & -13 \color{red}{-} (-5-5x) \\\Leftrightarrow & -8x-12& = &-13+5+5x \\\Leftrightarrow & -8x \color{red}{-12} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -8x-5x& = &-8+12 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x-4)& = & -10 \color{red}{+} (-4+x) \\\Leftrightarrow & -15x-12& = &-10-4+x \\\Leftrightarrow & -15x \color{red}{-12} & = &-14 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -15x-x& = &-14+12 \\\Leftrightarrow & -16x& = &-2 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-2}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-1)& = & 4 \color{red}{-} (6-3x) \\\Leftrightarrow & -4x-4& = &4-6+3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -4x-3x& = &-2+4 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x-3)& = & 6 \color{red}{-} (7+4x) \\\Leftrightarrow & 15x-15& = &6-7-4x \\\Leftrightarrow & 15x \color{red}{-15} & = &-1 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 15x+4x& = &-1+15 \\\Leftrightarrow & 19x& = &14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x-3)& = & 11 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x-18& = &11+11-x \\\Leftrightarrow & 30x \color{red}{-18} & = &22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &22+18 \\\Leftrightarrow & 31x& = &40 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{40}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{40}{31} & & \\ & V = \left\{ \frac{40}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x+6)& = & -11 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+18& = &-11+6+x \\\Leftrightarrow & 12x \color{red}{+18} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &-5-18 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-6)& = & -13 \color{red}{-} (-4+x) \\\Leftrightarrow & -20x-30& = &-13+4-x \\\Leftrightarrow & -20x \color{red}{-30} & = &-9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &-9+30 \\\Leftrightarrow & -19x& = &21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-21}{19} & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+4)& = & 15 \color{red}{+} (13+x) \\\Leftrightarrow & -24x+16& = &15+13+x \\\Leftrightarrow & -24x \color{red}{+16} & = &28 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -24x-x& = &28-16 \\\Leftrightarrow & -25x& = &12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-12}{25} & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)