Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+5)& = & -6 \color{red}{-} (3-5x) \\\Leftrightarrow & 6x+30& = &-6-3+5x \\\Leftrightarrow & 6x \color{red}{+30} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & 6x-5x& = &-9-30 \\\Leftrightarrow & x& = &-39 \\ & V = \left\{ -39 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-3)& = & -7 \color{red}{+} (13+x) \\\Leftrightarrow & 12x-9& = &-7+13+x \\\Leftrightarrow & 12x \color{red}{-9} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &6+9 \\\Leftrightarrow & 11x& = &15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x+1)& = & -5 \color{red}{-} (9+x) \\\Leftrightarrow & -2x+2& = &-5-9-x \\\Leftrightarrow & -2x \color{red}{+2} & = &-14 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -2x+x& = &-14-2 \\\Leftrightarrow & -x& = &-16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-16}{ \color{red}{-1} } \\\Leftrightarrow & x = 16 & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-3)& = & -13 \color{red}{-} (11+x) \\\Leftrightarrow & 24x-18& = &-13-11-x \\\Leftrightarrow & 24x \color{red}{-18} & = &-24 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 24x+x& = &-24+18 \\\Leftrightarrow & 25x& = &-6 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-6}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-6}{25} & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x+2)& = & -14 \color{red}{-} (8+x) \\\Leftrightarrow & 8x+4& = &-14-8-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-22 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-22-4 \\\Leftrightarrow & 9x& = &-26 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-26}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-26}{9} & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-4)& = & -15 \color{red}{-} (-10-3x) \\\Leftrightarrow & 16x-16& = &-15+10+3x \\\Leftrightarrow & 16x \color{red}{-16} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & 16x-3x& = &-5+16 \\\Leftrightarrow & 13x& = &11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+6)& = & 12 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x+30& = &12+9-x \\\Leftrightarrow & -30x \color{red}{+30} & = &21 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &21-30 \\\Leftrightarrow & -29x& = &-9 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-9}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{9}{29} & & \\ & V = \left\{ \frac{9}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+3)& = & 4 \color{red}{+} (-1-5x) \\\Leftrightarrow & 16x+12& = &4-1-5x \\\Leftrightarrow & 16x \color{red}{+12} & = &3 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 16x+5x& = &3-12 \\\Leftrightarrow & 21x& = &-9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+1)& = & 3 \color{red}{-} (-5-5x) \\\Leftrightarrow & 18x+6& = &3+5+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &8 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &8-6 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-6)& = & -5 \color{red}{-} (-6+x) \\\Leftrightarrow & -18x-36& = &-5+6-x \\\Leftrightarrow & -18x \color{red}{-36} & = &1 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -18x+x& = &1+36 \\\Leftrightarrow & -17x& = &37 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{37}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-37}{17} & & \\ & V = \left\{ \frac{-37}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-2)& = & 1 \color{red}{-} (-13+3x) \\\Leftrightarrow & 8x-4& = &1+13-3x \\\Leftrightarrow & 8x \color{red}{-4} & = &14 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 8x+3x& = &14+4 \\\Leftrightarrow & 11x& = &18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+5)& = & 2 \color{red}{-} (5+x) \\\Leftrightarrow & -24x+20& = &2-5-x \\\Leftrightarrow & -24x \color{red}{+20} & = &-3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &-3-20 \\\Leftrightarrow & -23x& = &-23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-23}{ \color{red}{-23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)