Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+2)& = & 9 \color{red}{-} (-10-5x) \\\Leftrightarrow & -18x+6& = &9+10+5x \\\Leftrightarrow & -18x \color{red}{+6} & = &19 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -18x-5x& = &19-6 \\\Leftrightarrow & -23x& = &13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+3)& = & 5 \color{red}{+} (1-5x) \\\Leftrightarrow & 6x+6& = &5+1-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &6 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &6-6 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x+1)& = & -2 \color{red}{+} (9+x) \\\Leftrightarrow & -24x+4& = &-2+9+x \\\Leftrightarrow & -24x \color{red}{+4} & = &7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -24x-x& = &7-4 \\\Leftrightarrow & -25x& = &3 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{3}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-3}{25} & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-7)& = & 9 \color{red}{-} (-9+x) \\\Leftrightarrow & 4x-28& = &9+9-x \\\Leftrightarrow & 4x \color{red}{-28} & = &18 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 4x+x& = &18+28 \\\Leftrightarrow & 5x& = &46 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{46}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{46}{5} & & \\ & V = \left\{ \frac{46}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+2)& = & 2 \color{red}{+} (-7-4x) \\\Leftrightarrow & 25x+10& = &2-7-4x \\\Leftrightarrow & 25x \color{red}{+10} & = &-5 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &-5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & 25x+4x& = &-5-10 \\\Leftrightarrow & 29x& = &-15 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-15}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-15}{29} & & \\ & V = \left\{ \frac{-15}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x+4)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & 6x+8& = &-11-15-x \\\Leftrightarrow & 6x \color{red}{+8} & = &-26 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 6x+x& = &-26-8 \\\Leftrightarrow & 7x& = &-34 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-34}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-34}{7} & & \\ & V = \left\{ \frac{-34}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x+1)& = & 11 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x+4& = &11-2+x \\\Leftrightarrow & 12x \color{red}{+4} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &9-4 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x+4)& = & 12 \color{red}{+} (9+x) \\\Leftrightarrow & 12x+24& = &12+9+x \\\Leftrightarrow & 12x \color{red}{+24} & = &21 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &21-24 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x-7)& = & 9 \color{red}{-} (3+x) \\\Leftrightarrow & -12x-28& = &9-3-x \\\Leftrightarrow & -12x \color{red}{-28} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -12x+x& = &6+28 \\\Leftrightarrow & -11x& = &34 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{34}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-34}{11} & & \\ & V = \left\{ \frac{-34}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+5)& = & -8 \color{red}{-} (11+x) \\\Leftrightarrow & 8x+20& = &-8-11-x \\\Leftrightarrow & 8x \color{red}{+20} & = &-19 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 8x+x& = &-19-20 \\\Leftrightarrow & 9x& = &-39 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-39}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-2)& = & 8 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-4& = &8-8-x \\\Leftrightarrow & 12x \color{red}{-4} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &0+4 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+6)& = & 3 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x+24& = &3-3+x \\\Leftrightarrow & -20x \color{red}{+24} & = &0 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &0-24 \\\Leftrightarrow & -21x& = &-24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)