Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+2)& = & 8 \color{red}{+} (-9+x) \\\Leftrightarrow & 10x+4& = &8-9+x \\\Leftrightarrow & 10x \color{red}{+4} & = &-1 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 10x-x& = &-1-4 \\\Leftrightarrow & 9x& = &-5 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-5}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-5}{9} & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-2)& = & -8 \color{red}{-} (-8+x) \\\Leftrightarrow & 36x-12& = &-8+8-x \\\Leftrightarrow & 36x \color{red}{-12} & = &0 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 36x+x& = &0+12 \\\Leftrightarrow & 37x& = &12 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{12}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{12}{37} & & \\ & V = \left\{ \frac{12}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x+1)& = & 10 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x+5& = &10+4-x \\\Leftrightarrow & 20x \color{red}{+5} & = &14 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &14-5 \\\Leftrightarrow & 21x& = &9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x-7)& = & -1 \color{red}{+} (12+x) \\\Leftrightarrow & 24x-28& = &-1+12+x \\\Leftrightarrow & 24x \color{red}{-28} & = &11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 24x-x& = &11+28 \\\Leftrightarrow & 23x& = &39 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{39}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{39}{23} & & \\ & V = \left\{ \frac{39}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x+1)& = & 14 \color{red}{+} (-2+x) \\\Leftrightarrow & 30x+5& = &14-2+x \\\Leftrightarrow & 30x \color{red}{+5} & = &12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 30x-x& = &12-5 \\\Leftrightarrow & 29x& = &7 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{7}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{7}{29} & & \\ & V = \left\{ \frac{7}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-1)& = & 13 \color{red}{+} (-9+x) \\\Leftrightarrow & -24x-4& = &13-9+x \\\Leftrightarrow & -24x \color{red}{-4} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &4+4 \\\Leftrightarrow & -25x& = &8 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{8}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+1)& = & -11 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+3& = &-11-4+x \\\Leftrightarrow & -12x \color{red}{+3} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &-15-3 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x-4)& = & 1 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-16& = &1+13-x \\\Leftrightarrow & -12x \color{red}{-16} & = &14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -12x+x& = &14+16 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x+2)& = & -1 \color{red}{+} (4-5x) \\\Leftrightarrow & -6x+6& = &-1+4-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &3-6 \\\Leftrightarrow & -x& = &-3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-3}{ \color{red}{-1} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-2)& = & 13 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x-8& = &13+4-x \\\Leftrightarrow & 24x \color{red}{-8} & = &17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 24x+x& = &17+8 \\\Leftrightarrow & 25x& = &25 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{25}{ \color{red}{25} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+2)& = & -10 \color{red}{-} (14+x) \\\Leftrightarrow & 20x+8& = &-10-14-x \\\Leftrightarrow & 20x \color{red}{+8} & = &-24 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &-24-8 \\\Leftrightarrow & 21x& = &-32 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-32}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-32}{21} & & \\ & V = \left\{ \frac{-32}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x-3)& = & 1 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x-6& = &1+2-x \\\Leftrightarrow & -12x \color{red}{-6} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &3+6 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)