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There is no equation - only an expression. So there are no solutions (or solution intervals).
To determine if 3 is the solution to the equation (-13 - 1 = x - 15), we first simplify the left side: (-13 - 1 = -14). The equation then becomes (-14 = x - 15). Adding 15 to both sides gives (x = 1), not 3. Therefore, 3 is not the solution.
4
One solution. (cos x)2 - 2cos x = 3 Factor: (cos x - 3)(cos x + 1)= 0 cos x = {-1, 3} Solve: For cos x = -1, x = 180 deg No solution for cos x = 3
To solve the inequality ( x^2 < 9 ), we first rewrite it as ( x^2 - 9 < 0 ), which factors to ( (x - 3)(x + 3) < 0 ). The critical points are ( x = -3 ) and ( x = 3 ). Analyzing the intervals, we find that the solution to the inequality is ( -3 < x < 3 ). Therefore, the values of ( x ) that satisfy the inequality are those in the open interval ( (-3, 3) ).
There is no equation - only an expression. So there are no solutions (or solution intervals).
x+1=x+2 x=1+2+x 0x=1+2 0x=3 0x=/=3 (=/= means does not equal) so there is no solution
To determine if 3 is the solution to the equation (-13 - 1 = x - 15), we first simplify the left side: (-13 - 1 = -14). The equation then becomes (-14 = x - 15). Adding 15 to both sides gives (x = 1), not 3. Therefore, 3 is not the solution.
2
An equation with the solution set 1 and 3 can be written in factored form as (x-1)(x-3) = 0. When expanded, this equation becomes x^2 - 4x + 3 = 0. Therefore, the equation x^2 - 4x + 3 = 0 has the solution set 1 and 3.
4
One solution. (cos x)2 - 2cos x = 3 Factor: (cos x - 3)(cos x + 1)= 0 cos x = {-1, 3} Solve: For cos x = -1, x = 180 deg No solution for cos x = 3
To solve the inequality ( x^2 < 9 ), we first rewrite it as ( x^2 - 9 < 0 ), which factors to ( (x - 3)(x + 3) < 0 ). The critical points are ( x = -3 ) and ( x = 3 ). Analyzing the intervals, we find that the solution to the inequality is ( -3 < x < 3 ). Therefore, the values of ( x ) that satisfy the inequality are those in the open interval ( (-3, 3) ).
x2 + x + 1 = 0 ∴ x2 + x + 1/4 = -3/4 ∴ (x + 1/2)2 = -3/4 ∴ x + 1/2 = ± √(-3/4) ∴ x = - 1/2 ± (i√3) / 2 ∴ x = (-1 ± i√3) / 2
2x2-7x+3 = 0 (2x-1)(x-3) = 0 x = 1/2 or x = 3
y = x - 1 y - x = 3 y = x - 1 y = x + 3 Since both equations represent straight lines that have equal slopes, 1, then the lines are parallel to each other. That is that the lines do not intersect, and the system of the equations does not have a solution.
Solution: x = 1/4 and x = -3.