Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x-4)& = & 4 \color{red}{-} (-13+3x) \\\Leftrightarrow & 8x-8& = &4+13-3x \\\Leftrightarrow & 8x \color{red}{-8} & = &17 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 8x+3x& = &17+8 \\\Leftrightarrow & 11x& = &25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-1)& = & 13 \color{red}{+} (7+x) \\\Leftrightarrow & -20x-5& = &13+7+x \\\Leftrightarrow & -20x \color{red}{-5} & = &20 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -20x-x& = &20+5 \\\Leftrightarrow & -21x& = &25 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{25}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-25}{21} & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x-7)& = & 11 \color{red}{-} (1+3x) \\\Leftrightarrow & -10x-35& = &11-1-3x \\\Leftrightarrow & -10x \color{red}{-35} & = &10 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & -10x+3x& = &10+35 \\\Leftrightarrow & -7x& = &45 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{45}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-45}{7} & & \\ & V = \left\{ \frac{-45}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x+7)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & -16x+28& = &-7-1+x \\\Leftrightarrow & -16x \color{red}{+28} & = &-8 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -16x-x& = &-8-28 \\\Leftrightarrow & -17x& = &-36 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-36}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{36}{17} & & \\ & V = \left\{ \frac{36}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-3)& = & -6 \color{red}{+} (-14+x) \\\Leftrightarrow & 18x-9& = &-6-14+x \\\Leftrightarrow & 18x \color{red}{-9} & = &-20 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 18x-x& = &-20+9 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-7)& = & -2 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-14& = &-2-6+x \\\Leftrightarrow & -12x \color{red}{-14} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -12x-x& = &-8+14 \\\Leftrightarrow & -13x& = &6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+4)& = & -3 \color{red}{-} (13+x) \\\Leftrightarrow & -20x+20& = &-3-13-x \\\Leftrightarrow & -20x \color{red}{+20} & = &-16 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -20x+x& = &-16-20 \\\Leftrightarrow & -19x& = &-36 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-36}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{36}{19} & & \\ & V = \left\{ \frac{36}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-2)& = & -4 \color{red}{-} (-9-3x) \\\Leftrightarrow & -10x-4& = &-4+9+3x \\\Leftrightarrow & -10x \color{red}{-4} & = &5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -10x-3x& = &5+4 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-4)& = & -5 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x-20& = &-5-4+x \\\Leftrightarrow & -30x \color{red}{-20} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &-9+20 \\\Leftrightarrow & -31x& = &11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-11}{31} & & \\ & V = \left\{ \frac{-11}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x-1)& = & 3 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-4& = &3+6+x \\\Leftrightarrow & -12x \color{red}{-4} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &9+4 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-2)& = & -14 \color{red}{-} (-1-5x) \\\Leftrightarrow & -8x-4& = &-14+1+5x \\\Leftrightarrow & -8x \color{red}{-4} & = &-13 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & -8x-5x& = &-13+4 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-7)& = & 3 \color{red}{-} (13+x) \\\Leftrightarrow & -24x-28& = &3-13-x \\\Leftrightarrow & -24x \color{red}{-28} & = &-10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &-10+28 \\\Leftrightarrow & -23x& = &18 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{18}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-18}{23} & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)