Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-2)& = & -4 \color{red}{+} (2+x) \\\Leftrightarrow & -18x-6& = &-4+2+x \\\Leftrightarrow & -18x \color{red}{-6} & = &-2 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &-2+6 \\\Leftrightarrow & -19x& = &4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+2)& = & -11 \color{red}{+} (-7-4x) \\\Leftrightarrow & 25x+10& = &-11-7-4x \\\Leftrightarrow & 25x \color{red}{+10} & = &-18 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &-18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & 25x+4x& = &-18-10 \\\Leftrightarrow & 29x& = &-28 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-28}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x+6)& = & -11 \color{red}{+} (5+x) \\\Leftrightarrow & 6x+36& = &-11+5+x \\\Leftrightarrow & 6x \color{red}{+36} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 6x-x& = &-6-36 \\\Leftrightarrow & 5x& = &-42 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-42}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-42}{5} & & \\ & V = \left\{ \frac{-42}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x-2)& = & 15 \color{red}{+} (-3+x) \\\Leftrightarrow & -2x-4& = &15-3+x \\\Leftrightarrow & -2x \color{red}{-4} & = &12 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &12+4 \\\Leftrightarrow & -3x& = &16 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{16}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-16}{3} & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x+4)& = & 1 \color{red}{-} (15+3x) \\\Leftrightarrow & -25x+20& = &1-15-3x \\\Leftrightarrow & -25x \color{red}{+20} & = &-14 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -25x+3x& = &-14-20 \\\Leftrightarrow & -22x& = &-34 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{-34}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-1)& = & 6 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-6& = &6-14+x \\\Leftrightarrow & -24x \color{red}{-6} & = &-8 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -24x-x& = &-8+6 \\\Leftrightarrow & -25x& = &-2 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-2}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x-3)& = & -12 \color{red}{-} (11+x) \\\Leftrightarrow & -12x-9& = &-12-11-x \\\Leftrightarrow & -12x \color{red}{-9} & = &-23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &-23+9 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x-3)& = & 8 \color{red}{-} (5+x) \\\Leftrightarrow & -24x-12& = &8-5-x \\\Leftrightarrow & -24x \color{red}{-12} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &3+12 \\\Leftrightarrow & -23x& = &15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+6)& = & 3 \color{red}{+} (11+x) \\\Leftrightarrow & 24x+36& = &3+11+x \\\Leftrightarrow & 24x \color{red}{+36} & = &14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 24x-x& = &14-36 \\\Leftrightarrow & 23x& = &-22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-2)& = & 5 \color{red}{-} (2+2x) \\\Leftrightarrow & 15x-6& = &5-2-2x \\\Leftrightarrow & 15x \color{red}{-6} & = &3 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & 15x+2x& = &3+6 \\\Leftrightarrow & 17x& = &9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x-3)& = & -11 \color{red}{-} (6+x) \\\Leftrightarrow & 6x-9& = &-11-6-x \\\Leftrightarrow & 6x \color{red}{-9} & = &-17 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 6x+x& = &-17+9 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x-4)& = & 14 \color{red}{-} (5+x) \\\Leftrightarrow & -8x-8& = &14-5-x \\\Leftrightarrow & -8x \color{red}{-8} & = &9 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &9+8 \\\Leftrightarrow & -7x& = &17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)