Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x+6)& = & 6 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x+36& = &6+11-x \\\Leftrightarrow & -24x \color{red}{+36} & = &17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -24x+x& = &17-36 \\\Leftrightarrow & -23x& = &-19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+6)& = & -12 \color{red}{+} (-6-2x) \\\Leftrightarrow & -25x+30& = &-12-6-2x \\\Leftrightarrow & -25x \color{red}{+30} & = &-18 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -25x+2x& = &-18-30 \\\Leftrightarrow & -23x& = &-48 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-48}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{48}{23} & & \\ & V = \left\{ \frac{48}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+4)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 24x+24& = &2-2-x \\\Leftrightarrow & 24x \color{red}{+24} & = &0 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &0-24 \\\Leftrightarrow & 25x& = &-24 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-24}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-24}{25} & & \\ & V = \left\{ \frac{-24}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+7)& = & -6 \color{red}{-} (-11-2x) \\\Leftrightarrow & 15x+21& = &-6+11+2x \\\Leftrightarrow & 15x \color{red}{+21} & = &5 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & 15x-2x& = &5-21 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-4)& = & 13 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-12& = &13-7-x \\\Leftrightarrow & -12x \color{red}{-12} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &6+12 \\\Leftrightarrow & -11x& = &18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-3)& = & 2 \color{red}{-} (-11+x) \\\Leftrightarrow & -30x-15& = &2+11-x \\\Leftrightarrow & -30x \color{red}{-15} & = &13 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -30x+x& = &13+15 \\\Leftrightarrow & -29x& = &28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-6)& = & 11 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x-36& = &11+14-x \\\Leftrightarrow & 6x \color{red}{-36} & = &25 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 6x+x& = &25+36 \\\Leftrightarrow & 7x& = &61 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{61}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{61}{7} & & \\ & V = \left\{ \frac{61}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x-2)& = & -14 \color{red}{+} (3+x) \\\Leftrightarrow & -12x-8& = &-14+3+x \\\Leftrightarrow & -12x \color{red}{-8} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &-11+8 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-5)& = & -15 \color{red}{-} (12+3x) \\\Leftrightarrow & -20x-25& = &-15-12-3x \\\Leftrightarrow & -20x \color{red}{-25} & = &-27 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &-27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & -20x+3x& = &-27+25 \\\Leftrightarrow & -17x& = &-2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+7)& = & -10 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x+35& = &-10-4+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &-14 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &-14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &-14-35 \\\Leftrightarrow & 13x& = &-49 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-49}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-49}{13} & & \\ & V = \left\{ \frac{-49}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-7)& = & 11 \color{red}{+} (13+x) \\\Leftrightarrow & 8x-28& = &11+13+x \\\Leftrightarrow & 8x \color{red}{-28} & = &24 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 8x-x& = &24+28 \\\Leftrightarrow & 7x& = &52 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{52}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{52}{7} & & \\ & V = \left\{ \frac{52}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-3)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-18& = &-2+14-x \\\Leftrightarrow & -12x \color{red}{-18} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &12+18 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)