Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-4)& = & -6 \color{red}{+} (-10-5x) \\\Leftrightarrow & 6x-8& = &-6-10-5x \\\Leftrightarrow & 6x \color{red}{-8} & = &-16 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 6x+5x& = &-16+8 \\\Leftrightarrow & 11x& = &-8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-6)& = & 3 \color{red}{+} (-5+x) \\\Leftrightarrow & -10x-12& = &3-5+x \\\Leftrightarrow & -10x \color{red}{-12} & = &-2 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -10x-x& = &-2+12 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x+5)& = & -11 \color{red}{-} (-15+x) \\\Leftrightarrow & 10x+25& = &-11+15-x \\\Leftrightarrow & 10x \color{red}{+25} & = &4 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 10x+x& = &4-25 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+5)& = & 15 \color{red}{-} (-8-2x) \\\Leftrightarrow & 3x+15& = &15+8+2x \\\Leftrightarrow & 3x \color{red}{+15} & = &23 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 3x-2x& = &23-15 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x-5)& = & 12 \color{red}{-} (6+x) \\\Leftrightarrow & 6x-10& = &12-6-x \\\Leftrightarrow & 6x \color{red}{-10} & = &6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 6x+x& = &6+10 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x-6)& = & -15 \color{red}{+} (-7+x) \\\Leftrightarrow & -8x-12& = &-15-7+x \\\Leftrightarrow & -8x \color{red}{-12} & = &-22 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &-22+12 \\\Leftrightarrow & -9x& = &-10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+2)& = & -6 \color{red}{+} (2+x) \\\Leftrightarrow & 36x+12& = &-6+2+x \\\Leftrightarrow & 36x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 36x-x& = &-4-12 \\\Leftrightarrow & 35x& = &-16 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-16}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-16}{35} & & \\ & V = \left\{ \frac{-16}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-2)& = & 5 \color{red}{+} (-9-5x) \\\Leftrightarrow & 6x-12& = &5-9-5x \\\Leftrightarrow & 6x \color{red}{-12} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 6x+5x& = &-4+12 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+4)& = & 8 \color{red}{+} (-9+3x) \\\Leftrightarrow & -5x+20& = &8-9+3x \\\Leftrightarrow & -5x \color{red}{+20} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -5x-3x& = &-1-20 \\\Leftrightarrow & -8x& = &-21 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-21}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{21}{8} & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+1)& = & 9 \color{red}{-} (-8+x) \\\Leftrightarrow & -20x+5& = &9+8-x \\\Leftrightarrow & -20x \color{red}{+5} & = &17 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -20x+x& = &17-5 \\\Leftrightarrow & -19x& = &12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (x-3)& = & 14 \color{red}{+} (6+x) \\\Leftrightarrow & 3x-9& = &14+6+x \\\Leftrightarrow & 3x \color{red}{-9} & = &20 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 3x-x& = &20+9 \\\Leftrightarrow & 2x& = &29 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{29}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{29}{2} & & \\ & V = \left\{ \frac{29}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-4)& = & -1 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x-24& = &-1+15-x \\\Leftrightarrow & 12x \color{red}{-24} & = &14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &14+24 \\\Leftrightarrow & 13x& = &38 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{38}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{38}{13} & & \\ & V = \left\{ \frac{38}{13} \right\} & \\\end{align}\)