Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-2)& = & -14 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-4& = &-14-11+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-25+4 \\\Leftrightarrow & -13x& = &-21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+4)& = & 12 \color{red}{-} (-2+x) \\\Leftrightarrow & 8x+16& = &12+2-x \\\Leftrightarrow & 8x \color{red}{+16} & = &14 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 8x+x& = &14-16 \\\Leftrightarrow & 9x& = &-2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-7)& = & -14 \color{red}{+} (-14+x) \\\Leftrightarrow & 6x-14& = &-14-14+x \\\Leftrightarrow & 6x \color{red}{-14} & = &-28 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 6x-x& = &-28+14 \\\Leftrightarrow & 5x& = &-14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+6)& = & -10 \color{red}{+} (8+x) \\\Leftrightarrow & -20x+24& = &-10+8+x \\\Leftrightarrow & -20x \color{red}{+24} & = &-2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &-2-24 \\\Leftrightarrow & -21x& = &-26 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-26}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x+4)& = & -7 \color{red}{+} (10+x) \\\Leftrightarrow & 20x+20& = &-7+10+x \\\Leftrightarrow & 20x \color{red}{+20} & = &3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &3-20 \\\Leftrightarrow & 19x& = &-17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x-2)& = & -10 \color{red}{+} (3+x) \\\Leftrightarrow & 20x-10& = &-10+3+x \\\Leftrightarrow & 20x \color{red}{-10} & = &-7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &-7+10 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-5)& = & -2 \color{red}{-} (-11+x) \\\Leftrightarrow & 4x-20& = &-2+11-x \\\Leftrightarrow & 4x \color{red}{-20} & = &9 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 4x+x& = &9+20 \\\Leftrightarrow & 5x& = &29 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{29}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{29}{5} & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x-6)& = & 1 \color{red}{-} (7+x) \\\Leftrightarrow & -2x-12& = &1-7-x \\\Leftrightarrow & -2x \color{red}{-12} & = &-6 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -2x+x& = &-6+12 \\\Leftrightarrow & -x& = &6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{6}{ \color{red}{-1} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-2)& = & -6 \color{red}{+} (3+x) \\\Leftrightarrow & 8x-4& = &-6+3+x \\\Leftrightarrow & 8x \color{red}{-4} & = &-3 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 8x-x& = &-3+4 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+5)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & 8x+20& = &7-13-x \\\Leftrightarrow & 8x \color{red}{+20} & = &-6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 8x+x& = &-6-20 \\\Leftrightarrow & 9x& = &-26 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-26}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-26}{9} & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-6)& = & -2 \color{red}{-} (13+x) \\\Leftrightarrow & -20x-30& = &-2-13-x \\\Leftrightarrow & -20x \color{red}{-30} & = &-15 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &-15+30 \\\Leftrightarrow & -19x& = &15 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{15}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-15}{19} & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x+7)& = & -8 \color{red}{+} (-1+x) \\\Leftrightarrow & 16x+28& = &-8-1+x \\\Leftrightarrow & 16x \color{red}{+28} & = &-9 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 16x-x& = &-9-28 \\\Leftrightarrow & 15x& = &-37 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-37}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-37}{15} & & \\ & V = \left\{ \frac{-37}{15} \right\} & \\\end{align}\)