Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 10x+\frac{4}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+28} & = & \color{red}{539x} +44 \\\Leftrightarrow & 770x \color{red}{+28} \color{blue}{-28} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{-28} \\\Leftrightarrow & 770x-539x& = & 44-28 \\\Leftrightarrow & \color{red}{231} x& = & 16 \\\Leftrightarrow & x = \frac{16}{231} & & \\ & V = \left\{ \frac{16}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+264} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 660x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 660x+275x& = & 20-264 \\\Leftrightarrow & \color{red}{935} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{935} & & \\ & V = \left\{ \frac{-244}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+24} & = & \color{red}{70x} +45 \\\Leftrightarrow & -300x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -300x-70x& = & 45-24 \\\Leftrightarrow & \color{red}{-370} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-370} & & \\\Leftrightarrow & x = \frac{-21}{370} & & \\ & V = \left\{ \frac{-21}{370} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{2}{9} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{180}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{+108} & = & \color{red}{180x} +10 \\\Leftrightarrow & -675x \color{red}{+108} \color{blue}{-108} \color{blue}{-180x} & = & \color{red}{180x} +10 \color{blue}{-180x} \color{blue}{-108} \\\Leftrightarrow & -675x-180x& = & 10-108 \\\Leftrightarrow & \color{red}{-855} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-855} & & \\\Leftrightarrow & x = \frac{98}{855} & & \\ & V = \left\{ \frac{98}{855} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+84} & = & \color{red}{-245x} +15 \\\Leftrightarrow & 700x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 700x+245x& = & 15-84 \\\Leftrightarrow & \color{red}{945} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{945} & & \\\Leftrightarrow & x = \frac{-23}{315} & & \\ & V = \left\{ \frac{-23}{315} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{10})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{9}{10}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-18} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{-18} \color{blue}{+18} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+18} \\\Leftrightarrow & -240x+100x& = & 45+18 \\\Leftrightarrow & \color{red}{-140} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-140} & & \\\Leftrightarrow & x = \frac{-9}{20} & & \\ & V = \left\{ \frac{-9}{20} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-168} & = & \color{red}{539x} +88 \\\Leftrightarrow & 1848x \color{red}{-168} \color{blue}{+168} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{+168} \\\Leftrightarrow & 1848x-539x& = & 88+168 \\\Leftrightarrow & \color{red}{1309} x& = & 256 \\\Leftrightarrow & x = \frac{256}{1309} & & \\ & V = \left\{ \frac{256}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+10} & = & \color{red}{-49x} +8 \\\Leftrightarrow & 70x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & 70x+49x& = & 8-10 \\\Leftrightarrow & \color{red}{119} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{119} & & \\ & V = \left\{ \frac{-2}{119} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 90x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 90x+75x& = & 10-36 \\\Leftrightarrow & \color{red}{165} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{165} & & \\ & V = \left\{ \frac{-26}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{3})& = & 3x+\frac{8}{7} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-140} & = & \color{red}{63x} +24 \\\Leftrightarrow & -168x \color{red}{-140} \color{blue}{+140} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{+140} \\\Leftrightarrow & -168x-63x& = & 24+140 \\\Leftrightarrow & \color{red}{-231} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-231} & & \\\Leftrightarrow & x = \frac{-164}{231} & & \\ & V = \left\{ \frac{-164}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{9})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 4x-\frac{4}{9}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{144}{ \color{blue}{36} }x- \frac{16}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 144x \color{red}{-16} & = & \color{red}{-252x} +27 \\\Leftrightarrow & 144x \color{red}{-16} \color{blue}{+16} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{+16} \\\Leftrightarrow & 144x+252x& = & 27+16 \\\Leftrightarrow & \color{red}{396} x& = & 43 \\\Leftrightarrow & x = \frac{43}{396} & & \\ & V = \left\{ \frac{43}{396} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-40} & = & \color{red}{98x} +49 \\\Leftrightarrow & 280x \color{red}{-40} \color{blue}{+40} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+40} \\\Leftrightarrow & 280x-98x& = & 49+40 \\\Leftrightarrow & \color{red}{182} x& = & 89 \\\Leftrightarrow & x = \frac{89}{182} & & \\ & V = \left\{ \frac{89}{182} \right\} & \\\end{align}\)