Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x-2)& = & 14 \color{red}{+} (-4-5x) \\\Leftrightarrow & 36x-12& = &14-4-5x \\\Leftrightarrow & 36x \color{red}{-12} & = &10 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 36x+5x& = &10+12 \\\Leftrightarrow & 41x& = &22 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{22}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{22}{41} & & \\ & V = \left\{ \frac{22}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-5)& = & 10 \color{red}{-} (-2+2x) \\\Leftrightarrow & 5x-25& = &10+2-2x \\\Leftrightarrow & 5x \color{red}{-25} & = &12 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & 5x+2x& = &12+25 \\\Leftrightarrow & 7x& = &37 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{37}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{37}{7} & & \\ & V = \left\{ \frac{37}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x-7)& = & 9 \color{red}{-} (1+3x) \\\Leftrightarrow & 10x-35& = &9-1-3x \\\Leftrightarrow & 10x \color{red}{-35} & = &8 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & 10x+3x& = &8+35 \\\Leftrightarrow & 13x& = &43 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{43}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{43}{13} & & \\ & V = \left\{ \frac{43}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-4)& = & -6 \color{red}{-} (-7+5x) \\\Leftrightarrow & 18x-24& = &-6+7-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &1+24 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-3)& = & -1 \color{red}{+} (9+4x) \\\Leftrightarrow & -5x-15& = &-1+9+4x \\\Leftrightarrow & -5x \color{red}{-15} & = &8 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & -5x-4x& = &8+15 \\\Leftrightarrow & -9x& = &23 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{23}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-23}{9} & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+2)& = & 1 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+6& = &1-7+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-6-6 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+7)& = & -11 \color{red}{-} (-12+3x) \\\Leftrightarrow & -5x+35& = &-11+12-3x \\\Leftrightarrow & -5x \color{red}{+35} & = &1 \color{red}{-3x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & -5x+3x& = &1-35 \\\Leftrightarrow & -2x& = &-34 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-34}{ \color{red}{-2} } \\\Leftrightarrow & x = 17 & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+4)& = & 12 \color{red}{+} (5+x) \\\Leftrightarrow & -30x+20& = &12+5+x \\\Leftrightarrow & -30x \color{red}{+20} & = &17 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &17-20 \\\Leftrightarrow & -31x& = &-3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x-4)& = & -14 \color{red}{-} (-4+5x) \\\Leftrightarrow & -6x-8& = &-14+4-5x \\\Leftrightarrow & -6x \color{red}{-8} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -6x+5x& = &-10+8 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+3)& = & -2 \color{red}{+} (15+x) \\\Leftrightarrow & 30x+15& = &-2+15+x \\\Leftrightarrow & 30x \color{red}{+15} & = &13 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 30x-x& = &13-15 \\\Leftrightarrow & 29x& = &-2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x+1)& = & 6 \color{red}{+} (6+5x) \\\Leftrightarrow & 4x+2& = &6+6+5x \\\Leftrightarrow & 4x \color{red}{+2} & = &12 \color{red}{+5x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 4x-5x& = &12-2 \\\Leftrightarrow & -x& = &10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{10}{ \color{red}{-1} } \\\Leftrightarrow & x = -10 & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x-5)& = & -12 \color{red}{+} (13+5x) \\\Leftrightarrow & 24x-20& = &-12+13+5x \\\Leftrightarrow & 24x \color{red}{-20} & = &1 \color{red}{+5x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & 24x-5x& = &1+20 \\\Leftrightarrow & 19x& = &21 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{21}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)