Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-7)& = & -1 \color{red}{+} (13+x) \\\Leftrightarrow & 30x-42& = &-1+13+x \\\Leftrightarrow & 30x \color{red}{-42} & = &12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &12+42 \\\Leftrightarrow & 29x& = &54 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{54}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{54}{29} & & \\ & V = \left\{ \frac{54}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-1)& = & 4 \color{red}{-} (-12+x) \\\Leftrightarrow & -15x-5& = &4+12-x \\\Leftrightarrow & -15x \color{red}{-5} & = &16 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -15x+x& = &16+5 \\\Leftrightarrow & -14x& = &21 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{21}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x+2)& = & -3 \color{red}{+} (11+x) \\\Leftrightarrow & -20x+10& = &-3+11+x \\\Leftrightarrow & -20x \color{red}{+10} & = &8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &8-10 \\\Leftrightarrow & -21x& = &-2 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-2}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+4)& = & -1 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+16& = &-1-4-x \\\Leftrightarrow & 12x \color{red}{+16} & = &-5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &-5-16 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-6)& = & -7 \color{red}{+} (-9+x) \\\Leftrightarrow & 18x-18& = &-7-9+x \\\Leftrightarrow & 18x \color{red}{-18} & = &-16 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &-16+18 \\\Leftrightarrow & 17x& = &2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-1)& = & -5 \color{red}{-} (14+x) \\\Leftrightarrow & 24x-4& = &-5-14-x \\\Leftrightarrow & 24x \color{red}{-4} & = &-19 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &-19+4 \\\Leftrightarrow & 25x& = &-15 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-15}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x+2)& = & 15 \color{red}{-} (11+x) \\\Leftrightarrow & -12x+4& = &15-11-x \\\Leftrightarrow & -12x \color{red}{+4} & = &4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &4-4 \\\Leftrightarrow & -11x& = &0 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{0}{ \color{red}{-11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x-7)& = & -11 \color{red}{+} (-4+x) \\\Leftrightarrow & -8x-28& = &-11-4+x \\\Leftrightarrow & -8x \color{red}{-28} & = &-15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -8x-x& = &-15+28 \\\Leftrightarrow & -9x& = &13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x-4)& = & -2 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-12& = &-2-7+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-9+12 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-2)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & -24x-12& = &-4-1-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-5+12 \\\Leftrightarrow & -23x& = &7 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{7}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-4)& = & -14 \color{red}{+} (5+x) \\\Leftrightarrow & -6x-24& = &-14+5+x \\\Leftrightarrow & -6x \color{red}{-24} & = &-9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -6x-x& = &-9+24 \\\Leftrightarrow & -7x& = &15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+4)& = & 12 \color{red}{+} (4+4x) \\\Leftrightarrow & -15x+20& = &12+4+4x \\\Leftrightarrow & -15x \color{red}{+20} & = &16 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -15x-4x& = &16-20 \\\Leftrightarrow & -19x& = &-4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)