Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+5)& = & -6 \color{red}{+} (7-5x) \\\Leftrightarrow & 18x+15& = &-6+7-5x \\\Leftrightarrow & 18x \color{red}{+15} & = &1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 18x+5x& = &1-15 \\\Leftrightarrow & 23x& = &-14 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-14}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-14}{23} & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x+3)& = & -13 \color{red}{-} (1-5x) \\\Leftrightarrow & -6x+18& = &-13-1+5x \\\Leftrightarrow & -6x \color{red}{+18} & = &-14 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -6x-5x& = &-14-18 \\\Leftrightarrow & -11x& = &-32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+1)& = & 11 \color{red}{+} (-15-5x) \\\Leftrightarrow & 8x+2& = &11-15-5x \\\Leftrightarrow & 8x \color{red}{+2} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-2} \\\Leftrightarrow & 8x+5x& = &-4-2 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-2)& = & -2 \color{red}{-} (-12-3x) \\\Leftrightarrow & 16x-8& = &-2+12+3x \\\Leftrightarrow & 16x \color{red}{-8} & = &10 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 16x-3x& = &10+8 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x-2)& = & -15 \color{red}{+} (-1+x) \\\Leftrightarrow & 24x-8& = &-15-1+x \\\Leftrightarrow & 24x \color{red}{-8} & = &-16 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 24x-x& = &-16+8 \\\Leftrightarrow & 23x& = &-8 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-8}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-8}{23} & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-7)& = & -2 \color{red}{-} (-3+x) \\\Leftrightarrow & -20x-35& = &-2+3-x \\\Leftrightarrow & -20x \color{red}{-35} & = &1 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -20x+x& = &1+35 \\\Leftrightarrow & -19x& = &36 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{36}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-36}{19} & & \\ & V = \left\{ \frac{-36}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x-7)& = & -13 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x-42& = &-13-6+x \\\Leftrightarrow & 24x \color{red}{-42} & = &-19 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &-19+42 \\\Leftrightarrow & 23x& = &23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{23}{ \color{red}{23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x-2)& = & -4 \color{red}{-} (2-5x) \\\Leftrightarrow & -18x-12& = &-4-2+5x \\\Leftrightarrow & -18x \color{red}{-12} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -18x-5x& = &-6+12 \\\Leftrightarrow & -23x& = &6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x-4)& = & -3 \color{red}{-} (-2+3x) \\\Leftrightarrow & 20x-16& = &-3+2-3x \\\Leftrightarrow & 20x \color{red}{-16} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 20x+3x& = &-1+16 \\\Leftrightarrow & 23x& = &15 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{15}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-5)& = & -12 \color{red}{+} (-1-5x) \\\Leftrightarrow & -18x-30& = &-12-1-5x \\\Leftrightarrow & -18x \color{red}{-30} & = &-13 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -18x+5x& = &-13+30 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-6)& = & 12 \color{red}{+} (1+x) \\\Leftrightarrow & 20x-24& = &12+1+x \\\Leftrightarrow & 20x \color{red}{-24} & = &13 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &13+24 \\\Leftrightarrow & 19x& = &37 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{37}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{37}{19} & & \\ & V = \left\{ \frac{37}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+7)& = & -1 \color{red}{+} (-9+x) \\\Leftrightarrow & -16x+28& = &-1-9+x \\\Leftrightarrow & -16x \color{red}{+28} & = &-10 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -16x-x& = &-10-28 \\\Leftrightarrow & -17x& = &-38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{38}{17} & & \\ & V = \left\{ \frac{38}{17} \right\} & \\\end{align}\)