Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+6)& = & -3 \color{red}{+} (-11+x) \\\Leftrightarrow & -30x+36& = &-3-11+x \\\Leftrightarrow & -30x \color{red}{+36} & = &-14 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -30x-x& = &-14-36 \\\Leftrightarrow & -31x& = &-50 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-50}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{50}{31} & & \\ & V = \left\{ \frac{50}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+2)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & 6x+4& = &6-11+x \\\Leftrightarrow & 6x \color{red}{+4} & = &-5 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 6x-x& = &-5-4 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x-3)& = & 5 \color{red}{-} (-7-5x) \\\Leftrightarrow & -16x-12& = &5+7+5x \\\Leftrightarrow & -16x \color{red}{-12} & = &12 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -16x-5x& = &12+12 \\\Leftrightarrow & -21x& = &24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-3)& = & 12 \color{red}{-} (-9-5x) \\\Leftrightarrow & -6x-18& = &12+9+5x \\\Leftrightarrow & -6x \color{red}{-18} & = &21 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &21 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -6x-5x& = &21+18 \\\Leftrightarrow & -11x& = &39 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{39}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-39}{11} & & \\ & V = \left\{ \frac{-39}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-6)& = & -14 \color{red}{-} (-13+3x) \\\Leftrightarrow & 16x-24& = &-14+13-3x \\\Leftrightarrow & 16x \color{red}{-24} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 16x+3x& = &-1+24 \\\Leftrightarrow & 19x& = &23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-3)& = & 1 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x-12& = &1-6+x \\\Leftrightarrow & 24x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &-5+12 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+4)& = & -4 \color{red}{+} (7-5x) \\\Leftrightarrow & 36x+24& = &-4+7-5x \\\Leftrightarrow & 36x \color{red}{+24} & = &3 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 36x+5x& = &3-24 \\\Leftrightarrow & 41x& = &-21 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-21}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-21}{41} & & \\ & V = \left\{ \frac{-21}{41} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x-3)& = & -14 \color{red}{+} (-3+x) \\\Leftrightarrow & -10x-15& = &-14-3+x \\\Leftrightarrow & -10x \color{red}{-15} & = &-17 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &-17+15 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x-7)& = & -11 \color{red}{+} (9+x) \\\Leftrightarrow & -24x-42& = &-11+9+x \\\Leftrightarrow & -24x \color{red}{-42} & = &-2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &-2+42 \\\Leftrightarrow & -25x& = &40 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{40}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+5)& = & -6 \color{red}{-} (13-5x) \\\Leftrightarrow & -18x+15& = &-6-13+5x \\\Leftrightarrow & -18x \color{red}{+15} & = &-19 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & -18x-5x& = &-19-15 \\\Leftrightarrow & -23x& = &-34 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-34}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{34}{23} & & \\ & V = \left\{ \frac{34}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x+6)& = & -9 \color{red}{+} (1+x) \\\Leftrightarrow & -8x+24& = &-9+1+x \\\Leftrightarrow & -8x \color{red}{+24} & = &-8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -8x-x& = &-8-24 \\\Leftrightarrow & -9x& = &-32 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-32}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{32}{9} & & \\ & V = \left\{ \frac{32}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x+5)& = & 7 \color{red}{-} (10+4x) \\\Leftrightarrow & -25x+25& = &7-10-4x \\\Leftrightarrow & -25x \color{red}{+25} & = &-3 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & -25x+4x& = &-3-25 \\\Leftrightarrow & -21x& = &-28 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-28}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)