Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+5)& = & 2 \color{red}{-} (3+x) \\\Leftrightarrow & -12x+10& = &2-3-x \\\Leftrightarrow & -12x \color{red}{+10} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &-1-10 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+7)& = & 2 \color{red}{-} (11-3x) \\\Leftrightarrow & -10x+35& = &2-11+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &-9-35 \\\Leftrightarrow & -13x& = &-44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{44}{13} & & \\ & V = \left\{ \frac{44}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-7)& = & -8 \color{red}{+} (9+x) \\\Leftrightarrow & -30x-35& = &-8+9+x \\\Leftrightarrow & -30x \color{red}{-35} & = &1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -30x-x& = &1+35 \\\Leftrightarrow & -31x& = &36 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{36}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-36}{31} & & \\ & V = \left\{ \frac{-36}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-4)& = & 4 \color{red}{+} (13+x) \\\Leftrightarrow & 20x-20& = &4+13+x \\\Leftrightarrow & 20x \color{red}{-20} & = &17 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &17+20 \\\Leftrightarrow & 19x& = &37 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{37}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{37}{19} & & \\ & V = \left\{ \frac{37}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-7)& = & -10 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x-42& = &-10-1+x \\\Leftrightarrow & 30x \color{red}{-42} & = &-11 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &-11+42 \\\Leftrightarrow & 29x& = &31 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{31}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{31}{29} & & \\ & V = \left\{ \frac{31}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x+7)& = & -15 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+14& = &-15+10-x \\\Leftrightarrow & -12x \color{red}{+14} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -12x+x& = &-5-14 \\\Leftrightarrow & -11x& = &-19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-5)& = & -2 \color{red}{-} (-3+3x) \\\Leftrightarrow & -20x-25& = &-2+3-3x \\\Leftrightarrow & -20x \color{red}{-25} & = &1 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & -20x+3x& = &1+25 \\\Leftrightarrow & -17x& = &26 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{26}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-26}{17} & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x+1)& = & 5 \color{red}{+} (-10+3x) \\\Leftrightarrow & 20x+5& = &5-10+3x \\\Leftrightarrow & 20x \color{red}{+5} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 20x-3x& = &-5-5 \\\Leftrightarrow & 17x& = &-10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-4)& = & -11 \color{red}{-} (7+3x) \\\Leftrightarrow & -20x-16& = &-11-7-3x \\\Leftrightarrow & -20x \color{red}{-16} & = &-18 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -20x+3x& = &-18+16 \\\Leftrightarrow & -17x& = &-2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x+3)& = & 9 \color{red}{+} (14+x) \\\Leftrightarrow & 6x+6& = &9+14+x \\\Leftrightarrow & 6x \color{red}{+6} & = &23 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &23-6 \\\Leftrightarrow & 5x& = &17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-7)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & -18x-21& = &-8-14+x \\\Leftrightarrow & -18x \color{red}{-21} & = &-22 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -18x-x& = &-22+21 \\\Leftrightarrow & -19x& = &-1 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-1}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+6)& = & -14 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x+24& = &-14+7-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-7-24 \\\Leftrightarrow & 25x& = &-31 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-31}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-31}{25} & & \\ & V = \left\{ \frac{-31}{25} \right\} & \\\end{align}\)