Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x+1)& = & 7 \color{red}{-} (12+x) \\\Leftrightarrow & -15x+3& = &7-12-x \\\Leftrightarrow & -15x \color{red}{+3} & = &-5 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -15x+x& = &-5-3 \\\Leftrightarrow & -14x& = &-8 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-8}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x-1)& = & 15 \color{red}{+} (14+x) \\\Leftrightarrow & -6x-6& = &15+14+x \\\Leftrightarrow & -6x \color{red}{-6} & = &29 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &29+6 \\\Leftrightarrow & -7x& = &35 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{35}{ \color{red}{-7} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x-2)& = & 13 \color{red}{-} (2+x) \\\Leftrightarrow & -12x-6& = &13-2-x \\\Leftrightarrow & -12x \color{red}{-6} & = &11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &11+6 \\\Leftrightarrow & -11x& = &17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-6)& = & -5 \color{red}{+} (-10-5x) \\\Leftrightarrow & 6x-18& = &-5-10-5x \\\Leftrightarrow & 6x \color{red}{-18} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 6x+5x& = &-15+18 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-7)& = & -6 \color{red}{+} (-13+x) \\\Leftrightarrow & 30x-42& = &-6-13+x \\\Leftrightarrow & 30x \color{red}{-42} & = &-19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &-19+42 \\\Leftrightarrow & 29x& = &23 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{23}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{23}{29} & & \\ & V = \left\{ \frac{23}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+4)& = & 2 \color{red}{-} (-11+x) \\\Leftrightarrow & 20x+20& = &2+11-x \\\Leftrightarrow & 20x \color{red}{+20} & = &13 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &13-20 \\\Leftrightarrow & 21x& = &-7 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-7}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x-1)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & 4x-2& = &-7-1+x \\\Leftrightarrow & 4x \color{red}{-2} & = &-8 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 4x-x& = &-8+2 \\\Leftrightarrow & 3x& = &-6 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-6}{ \color{red}{3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x-5)& = & -9 \color{red}{+} (7+x) \\\Leftrightarrow & 24x-20& = &-9+7+x \\\Leftrightarrow & 24x \color{red}{-20} & = &-2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &-2+20 \\\Leftrightarrow & 23x& = &18 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{18}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{18}{23} & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-1)& = & 1 \color{red}{-} (7-5x) \\\Leftrightarrow & 8x-2& = &1-7+5x \\\Leftrightarrow & 8x \color{red}{-2} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & 8x-5x& = &-6+2 \\\Leftrightarrow & 3x& = &-4 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-4}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x+2)& = & -8 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+4& = &-8-14-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-22 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-22-4 \\\Leftrightarrow & 13x& = &-26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-26}{ \color{red}{13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x+1)& = & -3 \color{red}{-} (2+x) \\\Leftrightarrow & -2x+2& = &-3-2-x \\\Leftrightarrow & -2x \color{red}{+2} & = &-5 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -2x+x& = &-5-2 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-1)& = & 9 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x-4& = &9+10-x \\\Leftrightarrow & -24x \color{red}{-4} & = &19 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &19+4 \\\Leftrightarrow & -23x& = &23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{23}{ \color{red}{-23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)