Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+4)& = & 12 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+8& = &12+6+x \\\Leftrightarrow & -12x \color{red}{+8} & = &18 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &18-8 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+6)& = & -6 \color{red}{-} (-11-3x) \\\Leftrightarrow & 25x+30& = &-6+11+3x \\\Leftrightarrow & 25x \color{red}{+30} & = &5 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 25x-3x& = &5-30 \\\Leftrightarrow & 22x& = &-25 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-25}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-25}{22} & & \\ & V = \left\{ \frac{-25}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+4)& = & -2 \color{red}{-} (-7+x) \\\Leftrightarrow & -15x+20& = &-2+7-x \\\Leftrightarrow & -15x \color{red}{+20} & = &5 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -15x+x& = &5-20 \\\Leftrightarrow & -14x& = &-15 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-15}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{15}{14} & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-3)& = & -15 \color{red}{-} (13+x) \\\Leftrightarrow & 6x-9& = &-15-13-x \\\Leftrightarrow & 6x \color{red}{-9} & = &-28 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 6x+x& = &-28+9 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-2)& = & -3 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-6& = &-3+14-x \\\Leftrightarrow & -12x \color{red}{-6} & = &11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &11+6 \\\Leftrightarrow & -11x& = &17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+6)& = & 11 \color{red}{-} (11+x) \\\Leftrightarrow & 12x+36& = &11-11-x \\\Leftrightarrow & 12x \color{red}{+36} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &0-36 \\\Leftrightarrow & 13x& = &-36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-3)& = & -10 \color{red}{+} (-4-3x) \\\Leftrightarrow & -4x-12& = &-10-4-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &-14 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &-14+12 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+6)& = & -11 \color{red}{+} (-14-5x) \\\Leftrightarrow & -18x+36& = &-11-14-5x \\\Leftrightarrow & -18x \color{red}{+36} & = &-25 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -18x+5x& = &-25-36 \\\Leftrightarrow & -13x& = &-61 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-61}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{61}{13} & & \\ & V = \left\{ \frac{61}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+2)& = & -6 \color{red}{-} (3+x) \\\Leftrightarrow & 12x+8& = &-6-3-x \\\Leftrightarrow & 12x \color{red}{+8} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &-9-8 \\\Leftrightarrow & 13x& = &-17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x-7)& = & -2 \color{red}{+} (4-3x) \\\Leftrightarrow & -10x-35& = &-2+4-3x \\\Leftrightarrow & -10x \color{red}{-35} & = &2 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & -10x+3x& = &2+35 \\\Leftrightarrow & -7x& = &37 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{37}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-37}{7} & & \\ & V = \left\{ \frac{-37}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+3)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & -12x+18& = &-6+13+x \\\Leftrightarrow & -12x \color{red}{+18} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &7-18 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-4)& = & 7 \color{red}{+} (14+x) \\\Leftrightarrow & -6x-24& = &7+14+x \\\Leftrightarrow & -6x \color{red}{-24} & = &21 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -6x-x& = &21+24 \\\Leftrightarrow & -7x& = &45 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{45}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-45}{7} & & \\ & V = \left\{ \frac{-45}{7} \right\} & \\\end{align}\)