Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+4)& = & -9 \color{red}{-} (14+x) \\\Leftrightarrow & -12x+8& = &-9-14-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-23-8 \\\Leftrightarrow & -11x& = &-31 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-31}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{31}{11} & & \\ & V = \left\{ \frac{31}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (3x-7)& = & -3 \color{red}{-} (-6-2x) \\\Leftrightarrow & 15x-35& = &-3+6+2x \\\Leftrightarrow & 15x \color{red}{-35} & = &3 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 15x-2x& = &3+35 \\\Leftrightarrow & 13x& = &38 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{38}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{38}{13} & & \\ & V = \left\{ \frac{38}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x-1)& = & -9 \color{red}{-} (3+3x) \\\Leftrightarrow & 2x-2& = &-9-3-3x \\\Leftrightarrow & 2x \color{red}{-2} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 2x+3x& = &-12+2 \\\Leftrightarrow & 5x& = &-10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-10}{ \color{red}{5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-7)& = & 11 \color{red}{+} (9+2x) \\\Leftrightarrow & 25x-35& = &11+9+2x \\\Leftrightarrow & 25x \color{red}{-35} & = &20 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &20 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 25x-2x& = &20+35 \\\Leftrightarrow & 23x& = &55 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{55}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{55}{23} & & \\ & V = \left\{ \frac{55}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-2)& = & 13 \color{red}{+} (5+x) \\\Leftrightarrow & 18x-6& = &13+5+x \\\Leftrightarrow & 18x \color{red}{-6} & = &18 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &18+6 \\\Leftrightarrow & 17x& = &24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{24}{17} & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-1)& = & 14 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-6& = &14+14-x \\\Leftrightarrow & 30x \color{red}{-6} & = &28 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &28+6 \\\Leftrightarrow & 31x& = &34 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{34}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{34}{31} & & \\ & V = \left\{ \frac{34}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+1)& = & -5 \color{red}{-} (-2+4x) \\\Leftrightarrow & 3x+3& = &-5+2-4x \\\Leftrightarrow & 3x \color{red}{+3} & = &-3 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 3x+4x& = &-3-3 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (3x-1)& = & -2 \color{red}{+} (5-5x) \\\Leftrightarrow & 18x-6& = &-2+5-5x \\\Leftrightarrow & 18x \color{red}{-6} & = &3 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 18x+5x& = &3+6 \\\Leftrightarrow & 23x& = &9 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{9}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x+7)& = & -5 \color{red}{-} (2-5x) \\\Leftrightarrow & -16x+28& = &-5-2+5x \\\Leftrightarrow & -16x \color{red}{+28} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-28} \\\Leftrightarrow & -16x-5x& = &-7-28 \\\Leftrightarrow & -21x& = &-35 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-35}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x-1)& = & -6 \color{red}{-} (2+x) \\\Leftrightarrow & -6x-3& = &-6-2-x \\\Leftrightarrow & -6x \color{red}{-3} & = &-8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -6x+x& = &-8+3 \\\Leftrightarrow & -5x& = &-5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-5}{ \color{red}{-5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-4)& = & 1 \color{red}{+} (11+x) \\\Leftrightarrow & 20x-16& = &1+11+x \\\Leftrightarrow & 20x \color{red}{-16} & = &12 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 20x-x& = &12+16 \\\Leftrightarrow & 19x& = &28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{28}{19} & & \\ & V = \left\{ \frac{28}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x-3)& = & -7 \color{red}{+} (9+x) \\\Leftrightarrow & -8x-6& = &-7+9+x \\\Leftrightarrow & -8x \color{red}{-6} & = &2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -8x-x& = &2+6 \\\Leftrightarrow & -9x& = &8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)