Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+6)& = & 14 \color{red}{-} (-5-5x) \\\Leftrightarrow & 8x+12& = &14+5+5x \\\Leftrightarrow & 8x \color{red}{+12} & = &19 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 8x-5x& = &19-12 \\\Leftrightarrow & 3x& = &7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+3)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & -9x+9& = &6-7+x \\\Leftrightarrow & -9x \color{red}{+9} & = &-1 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -9x-x& = &-1-9 \\\Leftrightarrow & -10x& = &-10 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-10}{ \color{red}{-10} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+3)& = & -4 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x+6& = &-4-2+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-6-6 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x-2)& = & 4 \color{red}{+} (9+x) \\\Leftrightarrow & -36x-12& = &4+9+x \\\Leftrightarrow & -36x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -36x-x& = &13+12 \\\Leftrightarrow & -37x& = &25 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{25}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-25}{37} & & \\ & V = \left\{ \frac{-25}{37} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x-3)& = & -5 \color{red}{-} (12-5x) \\\Leftrightarrow & -6x-6& = &-5-12+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &-17 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &-17+6 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x-1)& = & 4 \color{red}{+} (12-5x) \\\Leftrightarrow & -18x-6& = &4+12-5x \\\Leftrightarrow & -18x \color{red}{-6} & = &16 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -18x+5x& = &16+6 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+1)& = & 15 \color{red}{+} (13+4x) \\\Leftrightarrow & 9x+3& = &15+13+4x \\\Leftrightarrow & 9x \color{red}{+3} & = &28 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &28 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & 9x-4x& = &28-3 \\\Leftrightarrow & 5x& = &25 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{25}{ \color{red}{5} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-3)& = & -10 \color{red}{+} (1+x) \\\Leftrightarrow & -30x-18& = &-10+1+x \\\Leftrightarrow & -30x \color{red}{-18} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -30x-x& = &-9+18 \\\Leftrightarrow & -31x& = &9 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{9}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-9}{31} & & \\ & V = \left\{ \frac{-9}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+4)& = & 9 \color{red}{+} (11+x) \\\Leftrightarrow & -20x+16& = &9+11+x \\\Leftrightarrow & -20x \color{red}{+16} & = &20 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &20-16 \\\Leftrightarrow & -21x& = &4 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{4}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x-6)& = & -2 \color{red}{+} (-4+x) \\\Leftrightarrow & 6x-18& = &-2-4+x \\\Leftrightarrow & 6x \color{red}{-18} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 6x-x& = &-6+18 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x-2)& = & -4 \color{red}{+} (5+x) \\\Leftrightarrow & 25x-10& = &-4+5+x \\\Leftrightarrow & 25x \color{red}{-10} & = &1 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 25x-x& = &1+10 \\\Leftrightarrow & 24x& = &11 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{11}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{11}{24} & & \\ & V = \left\{ \frac{11}{24} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-2)& = & 11 \color{red}{+} (10+x) \\\Leftrightarrow & -20x-10& = &11+10+x \\\Leftrightarrow & -20x \color{red}{-10} & = &21 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -20x-x& = &21+10 \\\Leftrightarrow & -21x& = &31 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{31}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-31}{21} & & \\ & V = \left\{ \frac{-31}{21} \right\} & \\\end{align}\)