Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x+1)& = & -10 \color{red}{+} (5+3x) \\\Leftrightarrow & 2x+2& = &-10+5+3x \\\Leftrightarrow & 2x \color{red}{+2} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 2x-3x& = &-5-2 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-7)& = & 3 \color{red}{-} (-6+x) \\\Leftrightarrow & 25x-35& = &3+6-x \\\Leftrightarrow & 25x \color{red}{-35} & = &9 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 25x+x& = &9+35 \\\Leftrightarrow & 26x& = &44 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{44}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x+3)& = & -7 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x+6& = &-7-13+x \\\Leftrightarrow & 6x \color{red}{+6} & = &-20 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &-20-6 \\\Leftrightarrow & 5x& = &-26 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-26}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-26}{5} & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x+5)& = & 1 \color{red}{-} (9+x) \\\Leftrightarrow & 20x+25& = &1-9-x \\\Leftrightarrow & 20x \color{red}{+25} & = &-8 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 20x+x& = &-8-25 \\\Leftrightarrow & 21x& = &-33 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-33}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x-5)& = & -11 \color{red}{+} (7+3x) \\\Leftrightarrow & 10x-10& = &-11+7+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &-4+10 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-6)& = & -4 \color{red}{-} (15+4x) \\\Leftrightarrow & 15x-18& = &-4-15-4x \\\Leftrightarrow & 15x \color{red}{-18} & = &-19 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &-19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & 15x+4x& = &-19+18 \\\Leftrightarrow & 19x& = &-1 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-1}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-1}{19} & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x+6)& = & -6 \color{red}{+} (8-2x) \\\Leftrightarrow & 15x+30& = &-6+8-2x \\\Leftrightarrow & 15x \color{red}{+30} & = &2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & 15x+2x& = &2-30 \\\Leftrightarrow & 17x& = &-28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-28}{17} & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-3)& = & 12 \color{red}{-} (4+x) \\\Leftrightarrow & 12x-9& = &12-4-x \\\Leftrightarrow & 12x \color{red}{-9} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &8+9 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+5)& = & 15 \color{red}{+} (-14+x) \\\Leftrightarrow & -20x+25& = &15-14+x \\\Leftrightarrow & -20x \color{red}{+25} & = &1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &1-25 \\\Leftrightarrow & -21x& = &-24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x+2)& = & 13 \color{red}{+} (-7+x) \\\Leftrightarrow & -15x+10& = &13-7+x \\\Leftrightarrow & -15x \color{red}{+10} & = &6 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -15x-x& = &6-10 \\\Leftrightarrow & -16x& = &-4 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-4}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x+6)& = & -2 \color{red}{-} (9+x) \\\Leftrightarrow & -8x+24& = &-2-9-x \\\Leftrightarrow & -8x \color{red}{+24} & = &-11 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -8x+x& = &-11-24 \\\Leftrightarrow & -7x& = &-35 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-35}{ \color{red}{-7} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x-2)& = & 2 \color{red}{-} (10+x) \\\Leftrightarrow & -18x-12& = &2-10-x \\\Leftrightarrow & -18x \color{red}{-12} & = &-8 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &-8+12 \\\Leftrightarrow & -17x& = &4 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{4}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)