Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+4)& = & 5 \color{red}{+} (1-4x) \\\Leftrightarrow & 25x+20& = &5+1-4x \\\Leftrightarrow & 25x \color{red}{+20} & = &6 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 25x+4x& = &6-20 \\\Leftrightarrow & 29x& = &-14 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-14}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-14}{29} & & \\ & V = \left\{ \frac{-14}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-5)& = & 13 \color{red}{-} (15-2x) \\\Leftrightarrow & 15x-15& = &13-15+2x \\\Leftrightarrow & 15x \color{red}{-15} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 15x-2x& = &-2+15 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x+3)& = & 6 \color{red}{-} (11+x) \\\Leftrightarrow & -16x+12& = &6-11-x \\\Leftrightarrow & -16x \color{red}{+12} & = &-5 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -16x+x& = &-5-12 \\\Leftrightarrow & -15x& = &-17 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-17}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{17}{15} & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+2)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & 24x+8& = &-7-1+x \\\Leftrightarrow & 24x \color{red}{+8} & = &-8 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 24x-x& = &-8-8 \\\Leftrightarrow & 23x& = &-16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x-4)& = & -8 \color{red}{-} (12+x) \\\Leftrightarrow & 6x-12& = &-8-12-x \\\Leftrightarrow & 6x \color{red}{-12} & = &-20 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &-20+12 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+4)& = & 2 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x+16& = &2+15-x \\\Leftrightarrow & -12x \color{red}{+16} & = &17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &17-16 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x+4)& = & -2 \color{red}{+} (-10-3x) \\\Leftrightarrow & 4x+16& = &-2-10-3x \\\Leftrightarrow & 4x \color{red}{+16} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & 4x+3x& = &-12-16 \\\Leftrightarrow & 7x& = &-28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-28}{ \color{red}{7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-1)& = & 1 \color{red}{-} (11+x) \\\Leftrightarrow & -30x-6& = &1-11-x \\\Leftrightarrow & -30x \color{red}{-6} & = &-10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -30x+x& = &-10+6 \\\Leftrightarrow & -29x& = &-4 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-4}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-1)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x-6& = &-5-15+x \\\Leftrightarrow & 24x \color{red}{-6} & = &-20 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 24x-x& = &-20+6 \\\Leftrightarrow & 23x& = &-14 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-14}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-14}{23} & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-4)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & 10x-20& = &-6-7-x \\\Leftrightarrow & 10x \color{red}{-20} & = &-13 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 10x+x& = &-13+20 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x+6)& = & 11 \color{red}{-} (-1+x) \\\Leftrightarrow & -20x+30& = &11+1-x \\\Leftrightarrow & -20x \color{red}{+30} & = &12 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -20x+x& = &12-30 \\\Leftrightarrow & -19x& = &-18 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-18}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+5)& = & 10 \color{red}{+} (-5+x) \\\Leftrightarrow & 20x+20& = &10-5+x \\\Leftrightarrow & 20x \color{red}{+20} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &5-20 \\\Leftrightarrow & 19x& = &-15 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-15}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-15}{19} & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)