Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-4)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & 4x-8& = &14+15+x \\\Leftrightarrow & 4x \color{red}{-8} & = &29 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 4x-x& = &29+8 \\\Leftrightarrow & 3x& = &37 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{37}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{37}{3} & & \\ & V = \left\{ \frac{37}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x+6)& = & 10 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x+36& = &10+2-x \\\Leftrightarrow & -30x \color{red}{+36} & = &12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &12-36 \\\Leftrightarrow & -29x& = &-24 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-24}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-2)& = & 5 \color{red}{-} (8+x) \\\Leftrightarrow & 5x-10& = &5-8-x \\\Leftrightarrow & 5x \color{red}{-10} & = &-3 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 5x+x& = &-3+10 \\\Leftrightarrow & 6x& = &7 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{7}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{7}{6} & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-2x+7)& = & 10 \color{red}{-} (14+x) \\\Leftrightarrow & -10x+35& = &10-14-x \\\Leftrightarrow & -10x \color{red}{+35} & = &-4 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -10x+x& = &-4-35 \\\Leftrightarrow & -9x& = &-39 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-39}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-2)& = & -13 \color{red}{-} (-5-2x) \\\Leftrightarrow & -15x-6& = &-13+5+2x \\\Leftrightarrow & -15x \color{red}{-6} & = &-8 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -15x-2x& = &-8+6 \\\Leftrightarrow & -17x& = &-2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (4x+4)& = & 6 \color{red}{+} (-6+x) \\\Leftrightarrow & 8x+8& = &6-6+x \\\Leftrightarrow & 8x \color{red}{+8} & = &0 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 8x-x& = &0-8 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+4)& = & 8 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+24& = &8-9+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-1-24 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-4)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & -8x-8& = &4+5+x \\\Leftrightarrow & -8x \color{red}{-8} & = &9 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -8x-x& = &9+8 \\\Leftrightarrow & -9x& = &17 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{17}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x-7)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 24x-28& = &-10-3-x \\\Leftrightarrow & 24x \color{red}{-28} & = &-13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 24x+x& = &-13+28 \\\Leftrightarrow & 25x& = &15 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{15}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-5)& = & 2 \color{red}{-} (14+x) \\\Leftrightarrow & 12x-20& = &2-14-x \\\Leftrightarrow & 12x \color{red}{-20} & = &-12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 12x+x& = &-12+20 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-2)& = & -4 \color{red}{-} (-7+x) \\\Leftrightarrow & -18x-6& = &-4+7-x \\\Leftrightarrow & -18x \color{red}{-6} & = &3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &3+6 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+6)& = & 9 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x+24& = &9-15+x \\\Leftrightarrow & -20x \color{red}{+24} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &-6-24 \\\Leftrightarrow & -21x& = &-30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)