Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x+5)& = & -8 \color{red}{+} (-9-3x) \\\Leftrightarrow & 4x+20& = &-8-9-3x \\\Leftrightarrow & 4x \color{red}{+20} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 4x+3x& = &-17-20 \\\Leftrightarrow & 7x& = &-37 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-37}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-37}{7} & & \\ & V = \left\{ \frac{-37}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x+2)& = & -10 \color{red}{+} (15+x) \\\Leftrightarrow & 18x+12& = &-10+15+x \\\Leftrightarrow & 18x \color{red}{+12} & = &5 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 18x-x& = &5-12 \\\Leftrightarrow & 17x& = &-7 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-7}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-7}{17} & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-2)& = & -1 \color{red}{+} (10+x) \\\Leftrightarrow & 18x-12& = &-1+10+x \\\Leftrightarrow & 18x \color{red}{-12} & = &9 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 18x-x& = &9+12 \\\Leftrightarrow & 17x& = &21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+4)& = & 3 \color{red}{+} (2+x) \\\Leftrightarrow & -30x+20& = &3+2+x \\\Leftrightarrow & -30x \color{red}{+20} & = &5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &5-20 \\\Leftrightarrow & -31x& = &-15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{15}{31} & & \\ & V = \left\{ \frac{15}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+7)& = & -11 \color{red}{-} (6+x) \\\Leftrightarrow & -24x+28& = &-11-6-x \\\Leftrightarrow & -24x \color{red}{+28} & = &-17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &-17-28 \\\Leftrightarrow & -23x& = &-45 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-45}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{45}{23} & & \\ & V = \left\{ \frac{45}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+7)& = & -4 \color{red}{+} (-11+x) \\\Leftrightarrow & 30x+42& = &-4-11+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-15-42 \\\Leftrightarrow & 29x& = &-57 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-57}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-57}{29} & & \\ & V = \left\{ \frac{-57}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & -9 \color{red}{-} (8+x) \\\Leftrightarrow & -30x-20& = &-9-8-x \\\Leftrightarrow & -30x \color{red}{-20} & = &-17 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &-17+20 \\\Leftrightarrow & -29x& = &3 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{3}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x-4)& = & -14 \color{red}{+} (10-4x) \\\Leftrightarrow & -5x-20& = &-14+10-4x \\\Leftrightarrow & -5x \color{red}{-20} & = &-4 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -5x+4x& = &-4+20 \\\Leftrightarrow & -x& = &16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{16}{ \color{red}{-1} } \\\Leftrightarrow & x = -16 & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x-5)& = & -12 \color{red}{-} (6-5x) \\\Leftrightarrow & -18x-30& = &-12-6+5x \\\Leftrightarrow & -18x \color{red}{-30} & = &-18 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -18x-5x& = &-18+30 \\\Leftrightarrow & -23x& = &12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-2)& = & -11 \color{red}{-} (3+x) \\\Leftrightarrow & -12x-4& = &-11-3-x \\\Leftrightarrow & -12x \color{red}{-4} & = &-14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &-14+4 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x+5)& = & -4 \color{red}{-} (4-5x) \\\Leftrightarrow & -6x+10& = &-4-4+5x \\\Leftrightarrow & -6x \color{red}{+10} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & -6x-5x& = &-8-10 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-2)& = & 7 \color{red}{-} (5+x) \\\Leftrightarrow & -20x-10& = &7-5-x \\\Leftrightarrow & -20x \color{red}{-10} & = &2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &2+10 \\\Leftrightarrow & -19x& = &12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)