Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+5)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & -30x+30& = &8-14+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-6-30 \\\Leftrightarrow & -31x& = &-36 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-36}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{36}{31} & & \\ & V = \left\{ \frac{36}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+2)& = & -4 \color{red}{+} (-1+x) \\\Leftrightarrow & -25x+10& = &-4-1+x \\\Leftrightarrow & -25x \color{red}{+10} & = &-5 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -25x-x& = &-5-10 \\\Leftrightarrow & -26x& = &-15 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-15}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{15}{26} & & \\ & V = \left\{ \frac{15}{26} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-6)& = & -3 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x-12& = &-3+1-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-2+12 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+7)& = & 13 \color{red}{-} (-7-4x) \\\Leftrightarrow & 9x+21& = &13+7+4x \\\Leftrightarrow & 9x \color{red}{+21} & = &20 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 9x-4x& = &20-21 \\\Leftrightarrow & 5x& = &-1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x-3)& = & 5 \color{red}{-} (2+x) \\\Leftrightarrow & -30x-18& = &5-2-x \\\Leftrightarrow & -30x \color{red}{-18} & = &3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &3+18 \\\Leftrightarrow & -29x& = &21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-2)& = & 14 \color{red}{-} (-2+x) \\\Leftrightarrow & 10x-10& = &14+2-x \\\Leftrightarrow & 10x \color{red}{-10} & = &16 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 10x+x& = &16+10 \\\Leftrightarrow & 11x& = &26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-4)& = & 4 \color{red}{-} (-1+x) \\\Leftrightarrow & -6x-8& = &4+1-x \\\Leftrightarrow & -6x \color{red}{-8} & = &5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -6x+x& = &5+8 \\\Leftrightarrow & -5x& = &13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-3)& = & -2 \color{red}{-} (4+x) \\\Leftrightarrow & -8x-6& = &-2-4-x \\\Leftrightarrow & -8x \color{red}{-6} & = &-6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -8x+x& = &-6+6 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x-5)& = & -1 \color{red}{-} (3-2x) \\\Leftrightarrow & -15x-25& = &-1-3+2x \\\Leftrightarrow & -15x \color{red}{-25} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -15x-2x& = &-4+25 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-6)& = & -2 \color{red}{-} (10+x) \\\Leftrightarrow & 18x-18& = &-2-10-x \\\Leftrightarrow & 18x \color{red}{-18} & = &-12 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 18x+x& = &-12+18 \\\Leftrightarrow & 19x& = &6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x-4)& = & -4 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x-16& = &-4+5-x \\\Leftrightarrow & -12x \color{red}{-16} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -12x+x& = &1+16 \\\Leftrightarrow & -11x& = &17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-5)& = & 10 \color{red}{-} (-10+x) \\\Leftrightarrow & 30x-25& = &10+10-x \\\Leftrightarrow & 30x \color{red}{-25} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &20+25 \\\Leftrightarrow & 31x& = &45 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{45}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{45}{31} & & \\ & V = \left\{ \frac{45}{31} \right\} & \\\end{align}\)