Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+7)& = & -14 \color{red}{+} (-10+x) \\\Leftrightarrow & 20x+28& = &-14-10+x \\\Leftrightarrow & 20x \color{red}{+28} & = &-24 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 20x-x& = &-24-28 \\\Leftrightarrow & 19x& = &-52 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-52}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-52}{19} & & \\ & V = \left\{ \frac{-52}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x+6)& = & 5 \color{red}{-} (5-5x) \\\Leftrightarrow & -18x+18& = &5-5+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &0 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &0-18 \\\Leftrightarrow & -23x& = &-18 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-18}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{18}{23} & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x-1)& = & 15 \color{red}{+} (1-3x) \\\Leftrightarrow & -4x-2& = &15+1-3x \\\Leftrightarrow & -4x \color{red}{-2} & = &16 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -4x+3x& = &16+2 \\\Leftrightarrow & -x& = &18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{18}{ \color{red}{-1} } \\\Leftrightarrow & x = -18 & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-5)& = & -1 \color{red}{+} (-3+2x) \\\Leftrightarrow & 15x-25& = &-1-3+2x \\\Leftrightarrow & 15x \color{red}{-25} & = &-4 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & 15x-2x& = &-4+25 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-1)& = & 10 \color{red}{+} (-6+x) \\\Leftrightarrow & 20x-5& = &10-6+x \\\Leftrightarrow & 20x \color{red}{-5} & = &4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 20x-x& = &4+5 \\\Leftrightarrow & 19x& = &9 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{9}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{9}{19} & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+6)& = & 11 \color{red}{+} (2+x) \\\Leftrightarrow & 12x+24& = &11+2+x \\\Leftrightarrow & 12x \color{red}{+24} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &13-24 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-1)& = & 9 \color{red}{+} (-12-4x) \\\Leftrightarrow & 5x-5& = &9-12-4x \\\Leftrightarrow & 5x \color{red}{-5} & = &-3 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & 5x+4x& = &-3+5 \\\Leftrightarrow & 9x& = &2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x+7)& = & -14 \color{red}{+} (9+x) \\\Leftrightarrow & 30x+35& = &-14+9+x \\\Leftrightarrow & 30x \color{red}{+35} & = &-5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 30x-x& = &-5-35 \\\Leftrightarrow & 29x& = &-40 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-40}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-40}{29} & & \\ & V = \left\{ \frac{-40}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x+6)& = & -14 \color{red}{+} (13+x) \\\Leftrightarrow & 24x+24& = &-14+13+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-1-24 \\\Leftrightarrow & 23x& = &-25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-25}{23} & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+2)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & -16x+8& = &-3+9+x \\\Leftrightarrow & -16x \color{red}{+8} & = &6 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -16x-x& = &6-8 \\\Leftrightarrow & -17x& = &-2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x-3)& = & 9 \color{red}{-} (5+x) \\\Leftrightarrow & -4x-12& = &9-5-x \\\Leftrightarrow & -4x \color{red}{-12} & = &4 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -4x+x& = &4+12 \\\Leftrightarrow & -3x& = &16 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{16}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-16}{3} & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x+4)& = & -11 \color{red}{-} (7+x) \\\Leftrightarrow & -30x+24& = &-11-7-x \\\Leftrightarrow & -30x \color{red}{+24} & = &-18 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -30x+x& = &-18-24 \\\Leftrightarrow & -29x& = &-42 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-42}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{42}{29} & & \\ & V = \left\{ \frac{42}{29} \right\} & \\\end{align}\)