Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-7)& = & 2 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-42& = &2-7+x \\\Leftrightarrow & -12x \color{red}{-42} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -12x-x& = &-5+42 \\\Leftrightarrow & -13x& = &37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x+7)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & 8x+14& = &-10-6+x \\\Leftrightarrow & 8x \color{red}{+14} & = &-16 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 8x-x& = &-16-14 \\\Leftrightarrow & 7x& = &-30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+4)& = & -12 \color{red}{-} (15+x) \\\Leftrightarrow & 12x+12& = &-12-15-x \\\Leftrightarrow & 12x \color{red}{+12} & = &-27 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &-27-12 \\\Leftrightarrow & 13x& = &-39 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-39}{ \color{red}{13} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+5)& = & 2 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x+20& = &2+4-x \\\Leftrightarrow & 24x \color{red}{+20} & = &6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 24x+x& = &6-20 \\\Leftrightarrow & 25x& = &-14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-14}{25} & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x-5)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & -20x-20& = &10-3-x \\\Leftrightarrow & -20x \color{red}{-20} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -20x+x& = &7+20 \\\Leftrightarrow & -19x& = &27 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{27}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x+4)& = & -1 \color{red}{-} (14+x) \\\Leftrightarrow & 24x+16& = &-1-14-x \\\Leftrightarrow & 24x \color{red}{+16} & = &-15 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 24x+x& = &-15-16 \\\Leftrightarrow & 25x& = &-31 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-31}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-31}{25} & & \\ & V = \left\{ \frac{-31}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & 14 \color{red}{-} (3+x) \\\Leftrightarrow & -30x-20& = &14-3-x \\\Leftrightarrow & -30x \color{red}{-20} & = &11 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &11+20 \\\Leftrightarrow & -29x& = &31 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{31}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-31}{29} & & \\ & V = \left\{ \frac{-31}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-7)& = & 3 \color{red}{+} (13+x) \\\Leftrightarrow & 20x-28& = &3+13+x \\\Leftrightarrow & 20x \color{red}{-28} & = &16 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 20x-x& = &16+28 \\\Leftrightarrow & 19x& = &44 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{44}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{44}{19} & & \\ & V = \left\{ \frac{44}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x+3)& = & -11 \color{red}{-} (5-5x) \\\Leftrightarrow & -16x+12& = &-11-5+5x \\\Leftrightarrow & -16x \color{red}{+12} & = &-16 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -16x-5x& = &-16-12 \\\Leftrightarrow & -21x& = &-28 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-28}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-5)& = & 3 \color{red}{-} (8-3x) \\\Leftrightarrow & -4x-10& = &3-8+3x \\\Leftrightarrow & -4x \color{red}{-10} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -4x-3x& = &-5+10 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x+3)& = & -3 \color{red}{+} (-14-5x) \\\Leftrightarrow & -18x+9& = &-3-14-5x \\\Leftrightarrow & -18x \color{red}{+9} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -18x+5x& = &-17-9 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+4)& = & -1 \color{red}{-} (-13-2x) \\\Leftrightarrow & -15x+20& = &-1+13+2x \\\Leftrightarrow & -15x \color{red}{+20} & = &12 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -15x-2x& = &12-20 \\\Leftrightarrow & -17x& = &-8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{8}{17} & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)