Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-4)& = & -8 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x-24& = &-8-1+x \\\Leftrightarrow & -30x \color{red}{-24} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -30x-x& = &-9+24 \\\Leftrightarrow & -31x& = &15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-15}{31} & & \\ & V = \left\{ \frac{-15}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+5)& = & -14 \color{red}{+} (7+3x) \\\Leftrightarrow & -4x+20& = &-14+7+3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -4x-3x& = &-7-20 \\\Leftrightarrow & -7x& = &-27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-5)& = & 15 \color{red}{+} (-12-2x) \\\Leftrightarrow & 15x-25& = &15-12-2x \\\Leftrightarrow & 15x \color{red}{-25} & = &3 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & 15x+2x& = &3+25 \\\Leftrightarrow & 17x& = &28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{28}{17} & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+6)& = & -4 \color{red}{+} (-2+x) \\\Leftrightarrow & 8x+12& = &-4-2+x \\\Leftrightarrow & 8x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &-6-12 \\\Leftrightarrow & 7x& = &-18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+5)& = & 14 \color{red}{-} (-4+x) \\\Leftrightarrow & -20x+20& = &14+4-x \\\Leftrightarrow & -20x \color{red}{+20} & = &18 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -20x+x& = &18-20 \\\Leftrightarrow & -19x& = &-2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x+7)& = & -1 \color{red}{+} (10+x) \\\Leftrightarrow & -6x+14& = &-1+10+x \\\Leftrightarrow & -6x \color{red}{+14} & = &9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -6x-x& = &9-14 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x-5)& = & -5 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x-30& = &-5-14+x \\\Leftrightarrow & 12x \color{red}{-30} & = &-19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &-19+30 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x+2)& = & 13 \color{red}{-} (-3+3x) \\\Leftrightarrow & 10x+4& = &13+3-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &16 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &16-4 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+4)& = & 2 \color{red}{+} (14-4x) \\\Leftrightarrow & -5x+20& = &2+14-4x \\\Leftrightarrow & -5x \color{red}{+20} & = &16 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & -5x+4x& = &16-20 \\\Leftrightarrow & -x& = &-4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-4}{ \color{red}{-1} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-1)& = & -1 \color{red}{-} (-7-5x) \\\Leftrightarrow & 3x-3& = &-1+7+5x \\\Leftrightarrow & 3x \color{red}{-3} & = &6 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 3x-5x& = &6+3 \\\Leftrightarrow & -2x& = &9 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{9}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-9}{2} & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+7)& = & -7 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+28& = &-7+4-x \\\Leftrightarrow & -12x \color{red}{+28} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &-3-28 \\\Leftrightarrow & -11x& = &-31 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-31}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{31}{11} & & \\ & V = \left\{ \frac{31}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-7)& = & -6 \color{red}{+} (10+x) \\\Leftrightarrow & -9x-21& = &-6+10+x \\\Leftrightarrow & -9x \color{red}{-21} & = &4 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -9x-x& = &4+21 \\\Leftrightarrow & -10x& = &25 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{25}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)