Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+1)& = & -3 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+2& = &-3+5+x \\\Leftrightarrow & 12x \color{red}{+2} & = &2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &2-2 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x-3)& = & -10 \color{red}{-} (12+x) \\\Leftrightarrow & 10x-15& = &-10-12-x \\\Leftrightarrow & 10x \color{red}{-15} & = &-22 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 10x+x& = &-22+15 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+5)& = & -5 \color{red}{-} (1+x) \\\Leftrightarrow & 8x+10& = &-5-1-x \\\Leftrightarrow & 8x \color{red}{+10} & = &-6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &-6-10 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-2)& = & -2 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x-4& = &-2-14+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-16+4 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+6)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & -36x+36& = &10-3-x \\\Leftrightarrow & -36x \color{red}{+36} & = &7 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -36x+x& = &7-36 \\\Leftrightarrow & -35x& = &-29 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-29}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{29}{35} & & \\ & V = \left\{ \frac{29}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x-2)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & -18x-12& = &-4+10-x \\\Leftrightarrow & -18x \color{red}{-12} & = &6 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &6+12 \\\Leftrightarrow & -17x& = &18 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{18}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-18}{17} & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x+4)& = & -5 \color{red}{+} (-10-5x) \\\Leftrightarrow & -6x+8& = &-5-10-5x \\\Leftrightarrow & -6x \color{red}{+8} & = &-15 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -6x+5x& = &-15-8 \\\Leftrightarrow & -x& = &-23 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-23}{ \color{red}{-1} } \\\Leftrightarrow & x = 23 & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-5)& = & -12 \color{red}{-} (10+3x) \\\Leftrightarrow & 20x-25& = &-12-10-3x \\\Leftrightarrow & 20x \color{red}{-25} & = &-22 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &-22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 20x+3x& = &-22+25 \\\Leftrightarrow & 23x& = &3 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{3}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x-6)& = & -11 \color{red}{-} (5+x) \\\Leftrightarrow & 2x-12& = &-11-5-x \\\Leftrightarrow & 2x \color{red}{-12} & = &-16 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 2x+x& = &-16+12 \\\Leftrightarrow & 3x& = &-4 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-4}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x-3)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & -18x-9& = &2+10+x \\\Leftrightarrow & -18x \color{red}{-9} & = &12 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -18x-x& = &12+9 \\\Leftrightarrow & -19x& = &21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-21}{19} & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-1)& = & -6 \color{red}{-} (-2+x) \\\Leftrightarrow & 18x-6& = &-6+2-x \\\Leftrightarrow & 18x \color{red}{-6} & = &-4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 18x+x& = &-4+6 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x+7)& = & 7 \color{red}{+} (7+x) \\\Leftrightarrow & -12x+14& = &7+7+x \\\Leftrightarrow & -12x \color{red}{+14} & = &14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -12x-x& = &14-14 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)