Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x-3)& = & 14 \color{red}{-} (-3+x) \\\Leftrightarrow & 24x-12& = &14+3-x \\\Leftrightarrow & 24x \color{red}{-12} & = &17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &17+12 \\\Leftrightarrow & 25x& = &29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x+2)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & -12x+12& = &4+5+x \\\Leftrightarrow & -12x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &9-12 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x-5)& = & -11 \color{red}{-} (-5-3x) \\\Leftrightarrow & -10x-25& = &-11+5+3x \\\Leftrightarrow & -10x \color{red}{-25} & = &-6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -10x-3x& = &-6+25 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-2x-1)& = & 14 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-6& = &14-7+x \\\Leftrightarrow & -12x \color{red}{-6} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &7+6 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-5)& = & 15 \color{red}{-} (-4-5x) \\\Leftrightarrow & -8x-10& = &15+4+5x \\\Leftrightarrow & -8x \color{red}{-10} & = &19 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & -8x-5x& = &19+10 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+7)& = & 4 \color{red}{+} (14-4x) \\\Leftrightarrow & 5x+35& = &4+14-4x \\\Leftrightarrow & 5x \color{red}{+35} & = &18 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & 5x+4x& = &18-35 \\\Leftrightarrow & 9x& = &-17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+3)& = & -8 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x+15& = &-8-6+x \\\Leftrightarrow & 30x \color{red}{+15} & = &-14 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 30x-x& = &-14-15 \\\Leftrightarrow & 29x& = &-29 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-29}{ \color{red}{29} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-2)& = & 11 \color{red}{+} (13+x) \\\Leftrightarrow & 24x-12& = &11+13+x \\\Leftrightarrow & 24x \color{red}{-12} & = &24 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &24+12 \\\Leftrightarrow & 23x& = &36 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{36}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{36}{23} & & \\ & V = \left\{ \frac{36}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-3)& = & -4 \color{red}{+} (3+x) \\\Leftrightarrow & -2x-6& = &-4+3+x \\\Leftrightarrow & -2x \color{red}{-6} & = &-1 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -2x-x& = &-1+6 \\\Leftrightarrow & -3x& = &5 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{5}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x-3)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & 16x-12& = &6-11+x \\\Leftrightarrow & 16x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 16x-x& = &-5+12 \\\Leftrightarrow & 15x& = &7 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{7}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{7}{15} & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x+2)& = & -2 \color{red}{+} (8+x) \\\Leftrightarrow & 30x+12& = &-2+8+x \\\Leftrightarrow & 30x \color{red}{+12} & = &6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 30x-x& = &6-12 \\\Leftrightarrow & 29x& = &-6 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-6}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+6)& = & 11 \color{red}{+} (-1+x) \\\Leftrightarrow & -6x+36& = &11-1+x \\\Leftrightarrow & -6x \color{red}{+36} & = &10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -6x-x& = &10-36 \\\Leftrightarrow & -7x& = &-26 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-26}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)