Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+4)& = & 11 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x+24& = &11+6-5x \\\Leftrightarrow & 6x \color{red}{+24} & = &17 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 6x+5x& = &17-24 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-6)& = & -4 \color{red}{+} (-14-2x) \\\Leftrightarrow & 15x-18& = &-4-14-2x \\\Leftrightarrow & 15x \color{red}{-18} & = &-18 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 15x+2x& = &-18+18 \\\Leftrightarrow & 17x& = &0 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{0}{ \color{red}{17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+1)& = & -12 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x+6& = &-12+15-x \\\Leftrightarrow & -24x \color{red}{+6} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &3-6 \\\Leftrightarrow & -23x& = &-3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-1)& = & -4 \color{red}{+} (-10+x) \\\Leftrightarrow & -4x-2& = &-4-10+x \\\Leftrightarrow & -4x \color{red}{-2} & = &-14 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -4x-x& = &-14+2 \\\Leftrightarrow & -5x& = &-12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-2)& = & 15 \color{red}{-} (7-2x) \\\Leftrightarrow & -3x-6& = &15-7+2x \\\Leftrightarrow & -3x \color{red}{-6} & = &8 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -3x-2x& = &8+6 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x+3)& = & 15 \color{red}{+} (-6-5x) \\\Leftrightarrow & 6x+9& = &15-6-5x \\\Leftrightarrow & 6x \color{red}{+9} & = &9 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & 6x+5x& = &9-9 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x+5)& = & 9 \color{red}{+} (6+3x) \\\Leftrightarrow & 10x+10& = &9+6+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &15 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &15-10 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+6)& = & -5 \color{red}{-} (-13-2x) \\\Leftrightarrow & -15x+18& = &-5+13+2x \\\Leftrightarrow & -15x \color{red}{+18} & = &8 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & -15x-2x& = &8-18 \\\Leftrightarrow & -17x& = &-10 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-10}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-2)& = & 9 \color{red}{-} (9-3x) \\\Leftrightarrow & -16x-8& = &9-9+3x \\\Leftrightarrow & -16x \color{red}{-8} & = &0 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -16x-3x& = &0+8 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x+4)& = & 1 \color{red}{-} (7+x) \\\Leftrightarrow & -6x+24& = &1-7-x \\\Leftrightarrow & -6x \color{red}{+24} & = &-6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -6x+x& = &-6-24 \\\Leftrightarrow & -5x& = &-30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-30}{ \color{red}{-5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+2)& = & 7 \color{red}{-} (-3+4x) \\\Leftrightarrow & 25x+10& = &7+3-4x \\\Leftrightarrow & 25x \color{red}{+10} & = &10 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & 25x+4x& = &10-10 \\\Leftrightarrow & 29x& = &0 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{0}{ \color{red}{29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-1)& = & 13 \color{red}{-} (-5+x) \\\Leftrightarrow & 24x-6& = &13+5-x \\\Leftrightarrow & 24x \color{red}{-6} & = &18 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &18+6 \\\Leftrightarrow & 25x& = &24 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{24}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{24}{25} & & \\ & V = \left\{ \frac{24}{25} \right\} & \\\end{align}\)