Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-4)& = & -7 \color{red}{+} (-5+x) \\\Leftrightarrow & -18x-24& = &-7-5+x \\\Leftrightarrow & -18x \color{red}{-24} & = &-12 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -18x-x& = &-12+24 \\\Leftrightarrow & -19x& = &12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x-3)& = & -12 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x-6& = &-12+9-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-3+6 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x-2)& = & -11 \color{red}{-} (9-5x) \\\Leftrightarrow & -16x-8& = &-11-9+5x \\\Leftrightarrow & -16x \color{red}{-8} & = &-20 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -16x-5x& = &-20+8 \\\Leftrightarrow & -21x& = &-12 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-12}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+5)& = & 1 \color{red}{-} (5+x) \\\Leftrightarrow & 6x+15& = &1-5-x \\\Leftrightarrow & 6x \color{red}{+15} & = &-4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 6x+x& = &-4-15 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-5)& = & 15 \color{red}{+} (2+x) \\\Leftrightarrow & 30x-30& = &15+2+x \\\Leftrightarrow & 30x \color{red}{-30} & = &17 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &17+30 \\\Leftrightarrow & 29x& = &47 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{47}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{47}{29} & & \\ & V = \left\{ \frac{47}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x+5)& = & -6 \color{red}{-} (8-3x) \\\Leftrightarrow & 4x+20& = &-6-8+3x \\\Leftrightarrow & 4x \color{red}{+20} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & 4x-3x& = &-14-20 \\\Leftrightarrow & x& = &-34 \\ & V = \left\{ -34 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-3)& = & -15 \color{red}{+} (7+x) \\\Leftrightarrow & 18x-18& = &-15+7+x \\\Leftrightarrow & 18x \color{red}{-18} & = &-8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &-8+18 \\\Leftrightarrow & 17x& = &10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x-6)& = & 7 \color{red}{-} (-5+x) \\\Leftrightarrow & -8x-24& = &7+5-x \\\Leftrightarrow & -8x \color{red}{-24} & = &12 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -8x+x& = &12+24 \\\Leftrightarrow & -7x& = &36 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{36}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-36}{7} & & \\ & V = \left\{ \frac{-36}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+6)& = & -8 \color{red}{-} (-2-3x) \\\Leftrightarrow & -4x+12& = &-8+2+3x \\\Leftrightarrow & -4x \color{red}{+12} & = &-6 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -4x-3x& = &-6-12 \\\Leftrightarrow & -7x& = &-18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-3)& = & 3 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-12& = &3+7-x \\\Leftrightarrow & 12x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &10+12 \\\Leftrightarrow & 13x& = &22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+2)& = & 7 \color{red}{-} (-6+4x) \\\Leftrightarrow & 9x+6& = &7+6-4x \\\Leftrightarrow & 9x \color{red}{+6} & = &13 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & 9x+4x& = &13-6 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-3)& = & 8 \color{red}{-} (12+x) \\\Leftrightarrow & -12x-18& = &8-12-x \\\Leftrightarrow & -12x \color{red}{-18} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &-4+18 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)