Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-4)& = & -3 \color{red}{-} (13-2x) \\\Leftrightarrow & 3x-12& = &-3-13+2x \\\Leftrightarrow & 3x \color{red}{-12} & = &-16 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 3x-2x& = &-16+12 \\\Leftrightarrow & x& = &-4 \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-1)& = & 10 \color{red}{+} (6-5x) \\\Leftrightarrow & -36x-6& = &10+6-5x \\\Leftrightarrow & -36x \color{red}{-6} & = &16 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -36x+5x& = &16+6 \\\Leftrightarrow & -31x& = &22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-22}{31} & & \\ & V = \left\{ \frac{-22}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-2)& = & -8 \color{red}{-} (7+x) \\\Leftrightarrow & -20x-8& = &-8-7-x \\\Leftrightarrow & -20x \color{red}{-8} & = &-15 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -20x+x& = &-15+8 \\\Leftrightarrow & -19x& = &-7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-5)& = & -9 \color{red}{+} (9+x) \\\Leftrightarrow & -6x-10& = &-9+9+x \\\Leftrightarrow & -6x \color{red}{-10} & = &0 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -6x-x& = &0+10 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+6)& = & 15 \color{red}{+} (5+x) \\\Leftrightarrow & -24x+24& = &15+5+x \\\Leftrightarrow & -24x \color{red}{+24} & = &20 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &20-24 \\\Leftrightarrow & -25x& = &-4 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-4}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{4}{25} & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+4)& = & -9 \color{red}{+} (9+3x) \\\Leftrightarrow & 20x+20& = &-9+9+3x \\\Leftrightarrow & 20x \color{red}{+20} & = &0 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & 20x-3x& = &0-20 \\\Leftrightarrow & 17x& = &-20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-20}{17} & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-2)& = & 7 \color{red}{+} (13-5x) \\\Leftrightarrow & -6x-4& = &7+13-5x \\\Leftrightarrow & -6x \color{red}{-4} & = &20 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & -6x+5x& = &20+4 \\\Leftrightarrow & -x& = &24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{24}{ \color{red}{-1} } \\\Leftrightarrow & x = -24 & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x+7)& = & 14 \color{red}{+} (-13+x) \\\Leftrightarrow & 36x+42& = &14-13+x \\\Leftrightarrow & 36x \color{red}{+42} & = &1 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 36x-x& = &1-42 \\\Leftrightarrow & 35x& = &-41 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-41}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-41}{35} & & \\ & V = \left\{ \frac{-41}{35} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-2)& = & 8 \color{red}{-} (-10+x) \\\Leftrightarrow & 9x-6& = &8+10-x \\\Leftrightarrow & 9x \color{red}{-6} & = &18 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 9x+x& = &18+6 \\\Leftrightarrow & 10x& = &24 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{24}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+7)& = & -1 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x+42& = &-1+11-x \\\Leftrightarrow & 24x \color{red}{+42} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &10-42 \\\Leftrightarrow & 25x& = &-32 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-32}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-32}{25} & & \\ & V = \left\{ \frac{-32}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x-7)& = & -15 \color{red}{-} (-12+x) \\\Leftrightarrow & -18x-42& = &-15+12-x \\\Leftrightarrow & -18x \color{red}{-42} & = &-3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -18x+x& = &-3+42 \\\Leftrightarrow & -17x& = &39 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{39}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-39}{17} & & \\ & V = \left\{ \frac{-39}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+5)& = & 1 \color{red}{-} (14-4x) \\\Leftrightarrow & 25x+25& = &1-14+4x \\\Leftrightarrow & 25x \color{red}{+25} & = &-13 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 25x-4x& = &-13-25 \\\Leftrightarrow & 21x& = &-38 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-38}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-38}{21} & & \\ & V = \left\{ \frac{-38}{21} \right\} & \\\end{align}\)