Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -16x+\frac{12}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+84} & = & \color{red}{539x} +99 \\\Leftrightarrow & -1232x \color{red}{+84} \color{blue}{-84} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-84} \\\Leftrightarrow & -1232x-539x& = & 99-84 \\\Leftrightarrow & \color{red}{-1771} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-1771} & & \\\Leftrightarrow & x = \frac{-15}{1771} & & \\ & V = \left\{ \frac{-15}{1771} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{9})& = & -4x+\frac{10}{3} \\\Leftrightarrow & -15x+\frac{20}{9}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-135}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -135x \color{red}{+20} & = & \color{red}{-36x} +30 \\\Leftrightarrow & -135x \color{red}{+20} \color{blue}{-20} \color{blue}{+36x} & = & \color{red}{-36x} +30 \color{blue}{+36x} \color{blue}{-20} \\\Leftrightarrow & -135x+36x& = & 30-20 \\\Leftrightarrow & \color{red}{-99} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-99} & & \\\Leftrightarrow & x = \frac{-10}{99} & & \\ & V = \left\{ \frac{-10}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{11})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -25x+\frac{15}{11}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+45} & = & \color{red}{-264x} +44 \\\Leftrightarrow & -825x \color{red}{+45} \color{blue}{-45} \color{blue}{+264x} & = & \color{red}{-264x} +44 \color{blue}{+264x} \color{blue}{-45} \\\Leftrightarrow & -825x+264x& = & 44-45 \\\Leftrightarrow & \color{red}{-561} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-561} & & \\\Leftrightarrow & x = \frac{1}{561} & & \\ & V = \left\{ \frac{1}{561} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & -1848x+385x& = & 22-126 \\\Leftrightarrow & \color{red}{-1463} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1463} & & \\\Leftrightarrow & x = \frac{104}{1463} & & \\ & V = \left\{ \frac{104}{1463} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 20x-\frac{20}{9}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-80} & = & \color{red}{-108x} +27 \\\Leftrightarrow & 720x \color{red}{-80} \color{blue}{+80} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+80} \\\Leftrightarrow & 720x+108x& = & 27+80 \\\Leftrightarrow & \color{red}{828} x& = & 107 \\\Leftrightarrow & x = \frac{107}{828} & & \\ & V = \left\{ \frac{107}{828} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{9})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+40} & = & \color{red}{-405x} +36 \\\Leftrightarrow & -360x \color{red}{+40} \color{blue}{-40} \color{blue}{+405x} & = & \color{red}{-405x} +36 \color{blue}{+405x} \color{blue}{-40} \\\Leftrightarrow & -360x+405x& = & 36-40 \\\Leftrightarrow & \color{red}{45} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{4})& = & -2x+\frac{3}{7} \\\Leftrightarrow & 9x+\frac{15}{4}& = & -2x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{+105} & = & \color{red}{-56x} +12 \\\Leftrightarrow & 252x \color{red}{+105} \color{blue}{-105} \color{blue}{+56x} & = & \color{red}{-56x} +12 \color{blue}{+56x} \color{blue}{-105} \\\Leftrightarrow & 252x+56x& = & 12-105 \\\Leftrightarrow & \color{red}{308} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{308} & & \\ & V = \left\{ \frac{-93}{308} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{11})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -24x-\frac{30}{11}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-90} & = & \color{red}{165x} +77 \\\Leftrightarrow & -792x \color{red}{-90} \color{blue}{+90} \color{blue}{-165x} & = & \color{red}{165x} +77 \color{blue}{-165x} \color{blue}{+90} \\\Leftrightarrow & -792x-165x& = & 77+90 \\\Leftrightarrow & \color{red}{-957} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-957} & & \\\Leftrightarrow & x = \frac{-167}{957} & & \\ & V = \left\{ \frac{-167}{957} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+154} & = & \color{red}{297x} +12 \\\Leftrightarrow & 462x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & 462x-297x& = & 12-154 \\\Leftrightarrow & \color{red}{165} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{165} & & \\ & V = \left\{ \frac{-142}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 18x-\frac{24}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{-216} & = & \color{red}{693x} +88 \\\Leftrightarrow & 1782x \color{red}{-216} \color{blue}{+216} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{+216} \\\Leftrightarrow & 1782x-693x& = & 88+216 \\\Leftrightarrow & \color{red}{1089} x& = & 304 \\\Leftrightarrow & x = \frac{304}{1089} & & \\ & V = \left\{ \frac{304}{1089} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-140} & = & \color{red}{189x} +30 \\\Leftrightarrow & 168x \color{red}{-140} \color{blue}{+140} \color{blue}{-189x} & = & \color{red}{189x} +30 \color{blue}{-189x} \color{blue}{+140} \\\Leftrightarrow & 168x-189x& = & 30+140 \\\Leftrightarrow & \color{red}{-21} x& = & 170 \\\Leftrightarrow & x = \frac{170}{-21} & & \\\Leftrightarrow & x = \frac{-170}{21} & & \\ & V = \left\{ \frac{-170}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{3})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+20} & = & \color{red}{15x} +7 \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +7 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & 24x-15x& = & 7-20 \\\Leftrightarrow & \color{red}{9} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)