Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x-3)& = & 2 \color{red}{-} (-9+x) \\\Leftrightarrow & 36x-18& = &2+9-x \\\Leftrightarrow & 36x \color{red}{-18} & = &11 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 36x+x& = &11+18 \\\Leftrightarrow & 37x& = &29 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{29}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{29}{37} & & \\ & V = \left\{ \frac{29}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-1)& = & 5 \color{red}{-} (-4-5x) \\\Leftrightarrow & 18x-3& = &5+4+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &9 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &9+3 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x+5)& = & 12 \color{red}{+} (8-5x) \\\Leftrightarrow & 8x+20& = &12+8-5x \\\Leftrightarrow & 8x \color{red}{+20} & = &20 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-20} \\\Leftrightarrow & 8x+5x& = &20-20 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+2)& = & -10 \color{red}{-} (-5+x) \\\Leftrightarrow & 2x+4& = &-10+5-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-5-4 \\\Leftrightarrow & 3x& = &-9 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-9}{ \color{red}{3} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x+6)& = & 3 \color{red}{-} (1+x) \\\Leftrightarrow & 2x+12& = &3-1-x \\\Leftrightarrow & 2x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 2x+x& = &2-12 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x-5)& = & -14 \color{red}{+} (13+x) \\\Leftrightarrow & -12x-30& = &-14+13+x \\\Leftrightarrow & -12x \color{red}{-30} & = &-1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -12x-x& = &-1+30 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x+2)& = & 14 \color{red}{+} (11+x) \\\Leftrightarrow & 8x+8& = &14+11+x \\\Leftrightarrow & 8x \color{red}{+8} & = &25 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 8x-x& = &25-8 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x-6)& = & -1 \color{red}{+} (-13-2x) \\\Leftrightarrow & 15x-18& = &-1-13-2x \\\Leftrightarrow & 15x \color{red}{-18} & = &-14 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &-14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 15x+2x& = &-14+18 \\\Leftrightarrow & 17x& = &4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-7)& = & -5 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-14& = &-5+3-x \\\Leftrightarrow & -12x \color{red}{-14} & = &-2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -12x+x& = &-2+14 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+5)& = & 1 \color{red}{-} (4-2x) \\\Leftrightarrow & -15x+15& = &1-4+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &-3 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &-3-15 \\\Leftrightarrow & -17x& = &-18 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-18}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-1)& = & 12 \color{red}{-} (-13+x) \\\Leftrightarrow & -36x-6& = &12+13-x \\\Leftrightarrow & -36x \color{red}{-6} & = &25 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -36x+x& = &25+6 \\\Leftrightarrow & -35x& = &31 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{31}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-31}{35} & & \\ & V = \left\{ \frac{-31}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+5)& = & 2 \color{red}{-} (15+x) \\\Leftrightarrow & 6x+10& = &2-15-x \\\Leftrightarrow & 6x \color{red}{+10} & = &-13 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 6x+x& = &-13-10 \\\Leftrightarrow & 7x& = &-23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)