Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+2)& = & -12 \color{red}{+} (6-5x) \\\Leftrightarrow & -6x+12& = &-12+6-5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -6x+5x& = &-6-12 \\\Leftrightarrow & -x& = &-18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-18}{ \color{red}{-1} } \\\Leftrightarrow & x = 18 & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-4)& = & 10 \color{red}{+} (-13+x) \\\Leftrightarrow & 24x-24& = &10-13+x \\\Leftrightarrow & 24x \color{red}{-24} & = &-3 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &-3+24 \\\Leftrightarrow & 23x& = &21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+3)& = & -3 \color{red}{+} (-3+x) \\\Leftrightarrow & 15x+15& = &-3-3+x \\\Leftrightarrow & 15x \color{red}{+15} & = &-6 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 15x-x& = &-6-15 \\\Leftrightarrow & 14x& = &-21 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-21}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+7)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & 24x+28& = &-2+4+x \\\Leftrightarrow & 24x \color{red}{+28} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &2-28 \\\Leftrightarrow & 23x& = &-26 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-26}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-26}{23} & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+7)& = & -9 \color{red}{-} (1+5x) \\\Leftrightarrow & -36x+42& = &-9-1-5x \\\Leftrightarrow & -36x \color{red}{+42} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -36x+5x& = &-10-42 \\\Leftrightarrow & -31x& = &-52 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-52}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{52}{31} & & \\ & V = \left\{ \frac{52}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+1)& = & -10 \color{red}{+} (-5+3x) \\\Leftrightarrow & -8x+2& = &-10-5+3x \\\Leftrightarrow & -8x \color{red}{+2} & = &-15 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -8x-3x& = &-15-2 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+1)& = & 15 \color{red}{-} (-3-5x) \\\Leftrightarrow & 8x+2& = &15+3+5x \\\Leftrightarrow & 8x \color{red}{+2} & = &18 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 8x-5x& = &18-2 \\\Leftrightarrow & 3x& = &16 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{16}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{16}{3} & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x-4)& = & 14 \color{red}{-} (-4+x) \\\Leftrightarrow & -24x-16& = &14+4-x \\\Leftrightarrow & -24x \color{red}{-16} & = &18 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &18+16 \\\Leftrightarrow & -23x& = &34 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{34}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-34}{23} & & \\ & V = \left\{ \frac{-34}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-2)& = & 10 \color{red}{-} (-15+3x) \\\Leftrightarrow & 20x-10& = &10+15-3x \\\Leftrightarrow & 20x \color{red}{-10} & = &25 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 20x+3x& = &25+10 \\\Leftrightarrow & 23x& = &35 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{35}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{35}{23} & & \\ & V = \left\{ \frac{35}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+5)& = & -14 \color{red}{-} (5+x) \\\Leftrightarrow & -36x+30& = &-14-5-x \\\Leftrightarrow & -36x \color{red}{+30} & = &-19 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -36x+x& = &-19-30 \\\Leftrightarrow & -35x& = &-49 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-49}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-4)& = & -7 \color{red}{+} (-9+5x) \\\Leftrightarrow & -4x-8& = &-7-9+5x \\\Leftrightarrow & -4x \color{red}{-8} & = &-16 \color{red}{+5x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -4x-5x& = &-16+8 \\\Leftrightarrow & -9x& = &-8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-3)& = & 2 \color{red}{+} (2-5x) \\\Leftrightarrow & 18x-9& = &2+2-5x \\\Leftrightarrow & 18x \color{red}{-9} & = &4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 18x+5x& = &4+9 \\\Leftrightarrow & 23x& = &13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)