Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x-2)& = & 6 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x-8& = &6+15-x \\\Leftrightarrow & 20x \color{red}{-8} & = &21 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &21+8 \\\Leftrightarrow & 21x& = &29 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{29}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-4)& = & 11 \color{red}{+} (12-5x) \\\Leftrightarrow & 16x-16& = &11+12-5x \\\Leftrightarrow & 16x \color{red}{-16} & = &23 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+16} \\\Leftrightarrow & 16x+5x& = &23+16 \\\Leftrightarrow & 21x& = &39 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{39}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-3)& = & 7 \color{red}{-} (7+x) \\\Leftrightarrow & 4x-12& = &7-7-x \\\Leftrightarrow & 4x \color{red}{-12} & = &0 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 4x+x& = &0+12 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-5)& = & 1 \color{red}{-} (7-5x) \\\Leftrightarrow & -18x-30& = &1-7+5x \\\Leftrightarrow & -18x \color{red}{-30} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -18x-5x& = &-6+30 \\\Leftrightarrow & -23x& = &24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+6)& = & 15 \color{red}{-} (-2-5x) \\\Leftrightarrow & -18x+18& = &15+2+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &17 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &17-18 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-5)& = & 3 \color{red}{-} (9+3x) \\\Leftrightarrow & 10x-10& = &3-9-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &-6+10 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x-4)& = & -15 \color{red}{+} (-12-3x) \\\Leftrightarrow & 25x-20& = &-15-12-3x \\\Leftrightarrow & 25x \color{red}{-20} & = &-27 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 25x+3x& = &-27+20 \\\Leftrightarrow & 28x& = &-7 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-7}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-7)& = & -6 \color{red}{+} (8+x) \\\Leftrightarrow & 8x-14& = &-6+8+x \\\Leftrightarrow & 8x \color{red}{-14} & = &2 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 8x-x& = &2+14 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+3)& = & -1 \color{red}{+} (-12-5x) \\\Leftrightarrow & -36x+18& = &-1-12-5x \\\Leftrightarrow & -36x \color{red}{+18} & = &-13 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -36x+5x& = &-13-18 \\\Leftrightarrow & -31x& = &-31 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-31}{ \color{red}{-31} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x-6)& = & 8 \color{red}{+} (-7+2x) \\\Leftrightarrow & 15x-30& = &8-7+2x \\\Leftrightarrow & 15x \color{red}{-30} & = &1 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & 15x-2x& = &1+30 \\\Leftrightarrow & 13x& = &31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x+4)& = & 10 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x+24& = &10+7-x \\\Leftrightarrow & 24x \color{red}{+24} & = &17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &17-24 \\\Leftrightarrow & 25x& = &-7 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-7}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+2)& = & 7 \color{red}{-} (8+2x) \\\Leftrightarrow & 15x+10& = &7-8-2x \\\Leftrightarrow & 15x \color{red}{+10} & = &-1 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 15x+2x& = &-1-10 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)