Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x-2)& = & 13 \color{red}{-} (-14+x) \\\Leftrightarrow & -6x-4& = &13+14-x \\\Leftrightarrow & -6x \color{red}{-4} & = &27 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -6x+x& = &27+4 \\\Leftrightarrow & -5x& = &31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-31}{5} & & \\ & V = \left\{ \frac{-31}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x-4)& = & -9 \color{red}{-} (-8+x) \\\Leftrightarrow & -20x-16& = &-9+8-x \\\Leftrightarrow & -20x \color{red}{-16} & = &-1 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &-1+16 \\\Leftrightarrow & -19x& = &15 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{15}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-15}{19} & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-2)& = & 7 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-10& = &7-15+x \\\Leftrightarrow & 30x \color{red}{-10} & = &-8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 30x-x& = &-8+10 \\\Leftrightarrow & 29x& = &2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x-1)& = & 5 \color{red}{-} (1+x) \\\Leftrightarrow & 18x-3& = &5-1-x \\\Leftrightarrow & 18x \color{red}{-3} & = &4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 18x+x& = &4+3 \\\Leftrightarrow & 19x& = &7 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{7}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+5)& = & -4 \color{red}{+} (10+x) \\\Leftrightarrow & 20x+20& = &-4+10+x \\\Leftrightarrow & 20x \color{red}{+20} & = &6 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &6-20 \\\Leftrightarrow & 19x& = &-14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-2)& = & 12 \color{red}{-} (-12+x) \\\Leftrightarrow & 6x-4& = &12+12-x \\\Leftrightarrow & 6x \color{red}{-4} & = &24 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 6x+x& = &24+4 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-2)& = & -13 \color{red}{-} (4+x) \\\Leftrightarrow & -18x-6& = &-13-4-x \\\Leftrightarrow & -18x \color{red}{-6} & = &-17 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &-17+6 \\\Leftrightarrow & -17x& = &-11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-1)& = & -10 \color{red}{+} (-9+x) \\\Leftrightarrow & -6x-6& = &-10-9+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-19 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-19+6 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x-7)& = & -3 \color{red}{-} (13+x) \\\Leftrightarrow & 24x-28& = &-3-13-x \\\Leftrightarrow & 24x \color{red}{-28} & = &-16 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 24x+x& = &-16+28 \\\Leftrightarrow & 25x& = &12 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{12}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{12}{25} & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x+6)& = & 7 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+18& = &7+2-x \\\Leftrightarrow & -12x \color{red}{+18} & = &9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &9-18 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+7)& = & -3 \color{red}{-} (2+3x) \\\Leftrightarrow & -8x+14& = &-3-2-3x \\\Leftrightarrow & -8x \color{red}{+14} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -8x+3x& = &-5-14 \\\Leftrightarrow & -5x& = &-19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-1)& = & 6 \color{red}{+} (-12+x) \\\Leftrightarrow & 5x-5& = &6-12+x \\\Leftrightarrow & 5x \color{red}{-5} & = &-6 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 5x-x& = &-6+5 \\\Leftrightarrow & 4x& = &-1 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-1}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)