Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-6)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & -10x-30& = &9+6+x \\\Leftrightarrow & -10x \color{red}{-30} & = &15 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -10x-x& = &15+30 \\\Leftrightarrow & -11x& = &45 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{45}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-45}{11} & & \\ & V = \left\{ \frac{-45}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-7)& = & -6 \color{red}{+} (-6-5x) \\\Leftrightarrow & 36x-42& = &-6-6-5x \\\Leftrightarrow & 36x \color{red}{-42} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 36x+5x& = &-12+42 \\\Leftrightarrow & 41x& = &30 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{30}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{30}{41} & & \\ & V = \left\{ \frac{30}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-5)& = & -7 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x-25& = &-7+12-x \\\Leftrightarrow & 30x \color{red}{-25} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &5+25 \\\Leftrightarrow & 31x& = &30 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{30}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{30}{31} & & \\ & V = \left\{ \frac{30}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+5)& = & -3 \color{red}{-} (14-3x) \\\Leftrightarrow & 10x+25& = &-3-14+3x \\\Leftrightarrow & 10x \color{red}{+25} & = &-17 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &-17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & 10x-3x& = &-17-25 \\\Leftrightarrow & 7x& = &-42 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-42}{ \color{red}{7} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-4)& = & -3 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x-20& = &-3-14+x \\\Leftrightarrow & 30x \color{red}{-20} & = &-17 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 30x-x& = &-17+20 \\\Leftrightarrow & 29x& = &3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{3}{29} & & \\ & V = \left\{ \frac{3}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x+3)& = & 8 \color{red}{+} (-7+x) \\\Leftrightarrow & 2x+6& = &8-7+x \\\Leftrightarrow & 2x \color{red}{+6} & = &1 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 2x-x& = &1-6 \\\Leftrightarrow & x& = &-5 \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-1)& = & 10 \color{red}{+} (1+x) \\\Leftrightarrow & -18x-3& = &10+1+x \\\Leftrightarrow & -18x \color{red}{-3} & = &11 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -18x-x& = &11+3 \\\Leftrightarrow & -19x& = &14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+7)& = & -13 \color{red}{-} (7+x) \\\Leftrightarrow & -12x+28& = &-13-7-x \\\Leftrightarrow & -12x \color{red}{+28} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &-20-28 \\\Leftrightarrow & -11x& = &-48 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-48}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{48}{11} & & \\ & V = \left\{ \frac{48}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+5)& = & 6 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x+20& = &6+11+3x \\\Leftrightarrow & -4x \color{red}{+20} & = &17 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -4x-3x& = &17-20 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+4)& = & 15 \color{red}{+} (6+x) \\\Leftrightarrow & -15x+12& = &15+6+x \\\Leftrightarrow & -15x \color{red}{+12} & = &21 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -15x-x& = &21-12 \\\Leftrightarrow & -16x& = &9 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{9}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-9}{16} & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x-5)& = & -12 \color{red}{+} (11+3x) \\\Leftrightarrow & 25x-25& = &-12+11+3x \\\Leftrightarrow & 25x \color{red}{-25} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & 25x-3x& = &-1+25 \\\Leftrightarrow & 22x& = &24 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{24}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-4)& = & -4 \color{red}{+} (13+2x) \\\Leftrightarrow & 5x-20& = &-4+13+2x \\\Leftrightarrow & 5x \color{red}{-20} & = &9 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & 5x-2x& = &9+20 \\\Leftrightarrow & 3x& = &29 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{29}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{29}{3} & & \\ & V = \left\{ \frac{29}{3} \right\} & \\\end{align}\)