Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+5)& = & 2 \color{red}{+} (12+x) \\\Leftrightarrow & 4x+10& = &2+12+x \\\Leftrightarrow & 4x \color{red}{+10} & = &14 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 4x-x& = &14-10 \\\Leftrightarrow & 3x& = &4 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{4}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-7)& = & -1 \color{red}{+} (2+x) \\\Leftrightarrow & -18x-42& = &-1+2+x \\\Leftrightarrow & -18x \color{red}{-42} & = &1 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -18x-x& = &1+42 \\\Leftrightarrow & -19x& = &43 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{43}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-43}{19} & & \\ & V = \left\{ \frac{-43}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (6x+7)& = & -3 \color{red}{+} (1+x) \\\Leftrightarrow & 24x+28& = &-3+1+x \\\Leftrightarrow & 24x \color{red}{+28} & = &-2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &-2-28 \\\Leftrightarrow & 23x& = &-30 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-30}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-30}{23} & & \\ & V = \left\{ \frac{-30}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x+3)& = & 14 \color{red}{-} (-10+x) \\\Leftrightarrow & 6x+18& = &14+10-x \\\Leftrightarrow & 6x \color{red}{+18} & = &24 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &24-18 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x+4)& = & -11 \color{red}{+} (-3+x) \\\Leftrightarrow & 24x+24& = &-11-3+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-14-24 \\\Leftrightarrow & 23x& = &-38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x+1)& = & 1 \color{red}{+} (5-4x) \\\Leftrightarrow & 25x+5& = &1+5-4x \\\Leftrightarrow & 25x \color{red}{+5} & = &6 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & 25x+4x& = &6-5 \\\Leftrightarrow & 29x& = &1 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{1}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+3)& = & -2 \color{red}{-} (-8+x) \\\Leftrightarrow & 6x+6& = &-2+8-x \\\Leftrightarrow & 6x \color{red}{+6} & = &6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &6-6 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+7)& = & -12 \color{red}{-} (4-3x) \\\Leftrightarrow & 16x+28& = &-12-4+3x \\\Leftrightarrow & 16x \color{red}{+28} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 16x-3x& = &-16-28 \\\Leftrightarrow & 13x& = &-44 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-44}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-44}{13} & & \\ & V = \left\{ \frac{-44}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-1)& = & -9 \color{red}{-} (-7+4x) \\\Leftrightarrow & 3x-3& = &-9+7-4x \\\Leftrightarrow & 3x \color{red}{-3} & = &-2 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & 3x+4x& = &-2+3 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-4)& = & -11 \color{red}{+} (6+x) \\\Leftrightarrow & 20x-20& = &-11+6+x \\\Leftrightarrow & 20x \color{red}{-20} & = &-5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &-5+20 \\\Leftrightarrow & 19x& = &15 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{15}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{15}{19} & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+4)& = & -15 \color{red}{+} (10+x) \\\Leftrightarrow & 20x+20& = &-15+10+x \\\Leftrightarrow & 20x \color{red}{+20} & = &-5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &-5-20 \\\Leftrightarrow & 19x& = &-25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-25}{19} & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-5)& = & 13 \color{red}{+} (11+x) \\\Leftrightarrow & 6x-30& = &13+11+x \\\Leftrightarrow & 6x \color{red}{-30} & = &24 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 6x-x& = &24+30 \\\Leftrightarrow & 5x& = &54 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{54}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{54}{5} & & \\ & V = \left\{ \frac{54}{5} \right\} & \\\end{align}\)