Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & 450x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 450x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{345} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{345} & & \\ & V = \left\{ \frac{-26}{345} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{+105} & = & \color{red}{140x} +12 \\\Leftrightarrow & -252x \color{red}{+105} \color{blue}{-105} \color{blue}{-140x} & = & \color{red}{140x} +12 \color{blue}{-140x} \color{blue}{-105} \\\Leftrightarrow & -252x-140x& = & 12-105 \\\Leftrightarrow & \color{red}{-392} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-392} & & \\\Leftrightarrow & x = \frac{93}{392} & & \\ & V = \left\{ \frac{93}{392} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{16}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+16} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -36x \color{red}{+16} \color{blue}{-16} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{-16} \\\Leftrightarrow & -36x+15x& = & 4-16 \\\Leftrightarrow & \color{red}{-21} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-21} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{-275x} +25 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & -660x+275x& = & 25+132 \\\Leftrightarrow & \color{red}{-385} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-385} & & \\\Leftrightarrow & x = \frac{-157}{385} & & \\ & V = \left\{ \frac{-157}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{9})& = & 7x+\frac{7}{12} \\\Leftrightarrow & 8x+\frac{20}{9}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{288}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 288x \color{red}{+80} & = & \color{red}{252x} +21 \\\Leftrightarrow & 288x \color{red}{+80} \color{blue}{-80} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{-80} \\\Leftrightarrow & 288x-252x& = & 21-80 \\\Leftrightarrow & \color{red}{36} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{36} & & \\ & V = \left\{ \frac{-59}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+56} & = & \color{red}{-147x} +27 \\\Leftrightarrow & -336x \color{red}{+56} \color{blue}{-56} \color{blue}{+147x} & = & \color{red}{-147x} +27 \color{blue}{+147x} \color{blue}{-56} \\\Leftrightarrow & -336x+147x& = & 27-56 \\\Leftrightarrow & \color{red}{-189} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-189} & & \\\Leftrightarrow & x = \frac{29}{189} & & \\ & V = \left\{ \frac{29}{189} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{21}{8}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{-105} & = & \color{red}{80x} +48 \\\Leftrightarrow & 1400x \color{red}{-105} \color{blue}{+105} \color{blue}{-80x} & = & \color{red}{80x} +48 \color{blue}{-80x} \color{blue}{+105} \\\Leftrightarrow & 1400x-80x& = & 48+105 \\\Leftrightarrow & \color{red}{1320} x& = & 153 \\\Leftrightarrow & x = \frac{153}{1320} & & \\\Leftrightarrow & x = \frac{51}{440} & & \\ & V = \left\{ \frac{51}{440} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{9})& = & 2x+\frac{5}{12} \\\Leftrightarrow & 21x-\frac{35}{9}& = & 2x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{756}{ \color{blue}{36} }x- \frac{140}{ \color{blue}{36} })& = & (\frac{72}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 756x \color{red}{-140} & = & \color{red}{72x} +15 \\\Leftrightarrow & 756x \color{red}{-140} \color{blue}{+140} \color{blue}{-72x} & = & \color{red}{72x} +15 \color{blue}{-72x} \color{blue}{+140} \\\Leftrightarrow & 756x-72x& = & 15+140 \\\Leftrightarrow & \color{red}{684} x& = & 155 \\\Leftrightarrow & x = \frac{155}{684} & & \\ & V = \left\{ \frac{155}{684} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & -180x+75x& = & 10-36 \\\Leftrightarrow & \color{red}{-105} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-105} & & \\\Leftrightarrow & x = \frac{26}{105} & & \\ & V = \left\{ \frac{26}{105} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{-105x} +56 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & 252x+105x& = & 56+90 \\\Leftrightarrow & \color{red}{357} x& = & 146 \\\Leftrightarrow & x = \frac{146}{357} & & \\ & V = \left\{ \frac{146}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & -9x+\frac{5}{9} \\\Leftrightarrow & -8x+\frac{6}{5}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+54} & = & \color{red}{-405x} +25 \\\Leftrightarrow & -360x \color{red}{+54} \color{blue}{-54} \color{blue}{+405x} & = & \color{red}{-405x} +25 \color{blue}{+405x} \color{blue}{-54} \\\Leftrightarrow & -360x+405x& = & 25-54 \\\Leftrightarrow & \color{red}{45} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{45} & & \\ & V = \left\{ \frac{-29}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{27x} +10 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-20} \\\Leftrightarrow & -60x-27x& = & 10-20 \\\Leftrightarrow & \color{red}{-87} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-87} & & \\\Leftrightarrow & x = \frac{10}{87} & & \\ & V = \left\{ \frac{10}{87} \right\} & \\\end{align}\)